Sample Chapter

INSTANT DOWNLOAD COMPLETE TEST BANK WITH ANSWERS

Statistics For Business And Economics 12th Edition by McClave – Test Bank

Sample  Questions   

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) A recent report stated “Based on a sample of 160 truck drivers, there is evidence to indicate that, on

average, independent truck drivers earn more than company -hired truck drivers.” Does this statement describe descriptive or inferential statistics?

  1. A) Descriptive statistics B) Inferential statistics

1)                    

 

 

2) A survey of high school teenagers reported that 87% of those sampled are interested in pursuing a college education. Does this statement describe descriptive or inferential statistics?

  1. A) Inferential statistics B) Descriptive statistics

2)                    

 

 

3) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics?

  1. A) Descriptive statistics B) Inferential statistics

3)                    

 

 

4) From past figures, it is predicted that 30% of the registered voters will vote in the March primary.

Does this statement describe descriptive or inferential statistics?

  1. A) Inferential statistics B) Descriptive statistics

4)                    

 

 

5) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. The university is interested in using the information from the sample of 250 students collected to learn information about the entire student parking population. Would this be an application of descriptive or inferential statistics?

  1. A) Inferential statistics B) Descriptive statistics

5)                    

 

 

6) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Would this be an application of descriptive or inferential statistics?

  1. A) Inferential statistics B) Descriptive statistics

6)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

7) In a survey of 5000 high school students, 14% of those surveyed read at least one

best-seller each month. Give an example of a descriptive statement and an inferential statement that could be made based on this information.

7)                                    

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

8) Which of the following is not an element of descriptive statistical problems?

  1. A) predictions are made about a larger set of data
  2. B) patterns in a data set are identified
  3. C) information revealed in a data set is summarized
  4. D) data are displayed visually in graphs

8)                    

 

 

Answer the question True or False.

9) When we take data obtained from a sample and make generalizations or predictions about the

entire population, we are utilizing inferential statistics.

  1. A) True B) False

9)                    

 

 

10) Statistics involves two different processes, describing sets of data and drawing conclusions about the sets of data on the basis of sampling.

  1. A) True B) False

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) Parking at a university has become a problem. University administrators are interested in

determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 120 students and recorded how long it took each of them to find a parking spot. Identify the population of interest to the university administration.

  1. A) the 120 students about whom the data were collected
  2. B) the students who park at the university between 9 and 10 AM on Wednesdays
  3. C) the entire set of students who park at the university
  4. D) the entire set of faculty, staff, and students who park at the university

1)                    

 

 

2) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 270 students and recorded how long it took each of them to find a parking spot. Identify the variable of interest to the university administration.

  1. A) number of students who cannot find a spot
  2. B) students who drive cars on campus
  3. C) time to find a parking spot
  4. D) number of empty parking spots

2)                    

 

 

3) An assembly line is operating satisfactorily if fewer than 5% of the phones produced per day are defective. To check the quality of a day’s production, the company randomly samples 50 phones from a day’s production to test for defects. Define the population of interest to the manufacturer.

  1. A) all the phones produced during the day in question
  2. B) the 5% of the phones that are defective
  3. C) the 50 responses: defective or not defective
  4. D) the 50 phones sampled and tested

3)                    

 

 

4) An insurance company conducted a study to determine the percentage of cardiologists who had been sued for malpractice in the previous six years. The sample was randomly chosen from a national directory of doctors. What is the variable of interest in this study?

  1. A) all cardiologists in the directory
  2. B) the doctor’s area of expertise (i.e., cardiology, pediatrics, )
  3. C) the responses: have been sued/have not been sued for malpractice in the last six years
  4. D) the number of doctors who are cardiologists

4)                    

 

 

5) A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida coastline from environmental disasters. Forty-two hundred Florida residents were surveyed.Which of the following is the population used in the study?

  1. A) Florida residents willing to spend more tax dollars protecting the coastline from environmental disasters
  2. B) the 4200 Florida residents who were surveyed
  3. C) all Florida residents who lived along the coastline
  4. D) all Florida residents

5)                    

6) A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Forty-five hundred Florida residents were surveyed.Which of the following describes the variable of interest in the study?

  1. A) the response to the question “Do you live along the beach?”
  2. B) the response to the question, “Are you willing to spend more tax dollars on protecting the

Florida beaches from environmental disasters?”

  1. C) the 4500 Florida residents surveyed
  2. D) the response to the question “Do you use the beach?”

6)                    

 

 

7) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the population of interest to the university administration.

  1. A) a single student that parks at the university
  2. B) the 250 students that data was collected from
  3. C) the entire set of students that park at the university
  4. D) the parking time, defined to be the amount of time the student spent finding a parking spot

7)                    

 

 

8) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the sample of interest to the university administration.

  1. A) the parking time, defined to be the amount of time the student spent finding a parking spot
  2. B) a single student that parks at the university
  3. C) the entire set of students that park at the university
  4. D) the 250 students that data was collected from

8)                    

 

 

9) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the experimental unit of interest to the university administration.

  1. A) the 250 students that data was collected from
  2. B) the parking time, defined to be the amount of time the student spent finding a parking spot
  3. C) the entire set of students that park at the university
  4. D) a single student that parks at the university

9)                    

 

 

10) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the variable of interest to the university administration.

  1. A) a single student that parks at the university
  2. B) the parking time, defined to be the amount of time the student spent finding a parking spot
  3. C) the entire set of students that park at the university
  4. D) the 250 students that data was collected from

10)                 

11) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the population of interest for this study.

  1. A) the entire set of stocks that are traded on the NYSE B) the current price (or closing price) of a NYSE stock C) a single stock traded on the NYSE
  2. D) the 500 NYSE stocks that current prices were collected from

11)                 

 

 

12) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular

trading date) of the collected stocks using graphical and numerical techniques. Identify the sample of interest  for this study.

  1. A) the current price (or closing price) of a NYSE stock
  2. B) a single stock traded on the NYSE
  3. C) the entire set of stocks that are traded on the NYSE
  4. D) the 500 NYSE stocks that current prices were collected from

12)                 

 

 

13) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the experimental unit of interest  for this study.

  1. A) the 500 NYSE stocks that current prices were collected from
  2. B) a single stock traded on the NYSE
  3. C) the entire set of stocks that are traded on the NYSE D) the current price (or closing price) of a NYSE stock

13)                 

 

 

14) As part of an economics class project, students were asked to randomly select 500 New Your Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the variable of interest  for this study.

  1. A) the current price (or closing price) of a NYSE stock B) the entire set of stocks that are traded on the NYSE C) a single stock traded on the NYSE
  2. D) the 500 NYSE stocks that current prices were collected from

14)                 

 

 

15) A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the population of interest in this study.

  1. A) the response (Yes/No) to the question, “Have you taken at least one online class?”
  2. B) the 1500 community college students contacted
  3. C) the number of online classes a student has taken
  4. D) all community college students in the state of Georgia

15)                 

16) A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the variable of interest in this study.

  1. A) the number of online classes a student has taken
  2. B) the 1500 community college students contacted
  3. C) all community college students in the state of Georgia
  4. D) the response (Yes/No) to the question, “Have you taken at least one online class?”

16)                 

 

 

17) Which of the following is not typically an element of inferential statistical problems?

  1. A) sample B) variable of interest
  2. C) census D) measure of reliability

17)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

18) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 290 students and recorded how long it took each of them to find a parking spot. Identify the population, sample, and variable of interest to the administrators.

18)                                 

 

 

19) A quality inspector tested 66 copiers in an attempt to estimate the average failure rate of the copier model. His study indicated that the number of failures decreased from two years ago, indicating an increase in the reliability of the copiers. Describe the variable of interest to the inspector.

19)                                 

 

 

20) A high school guidance counselor analyzed data from a sample of 500 community colleges throughout the United States. One of his goals was to estimate the annual tuition costs of community colleges in the United States. Describe the population and variable of interest

to the guidance counselor.

20)                                 

 

 

21) Explain why it is not necessary to provide a measure of reliability when a census is used rather than a sample.

21)                                 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

22)  A variable is a characteristic or property of a population.

  1. A) True B) False

22)                 

 

 

23) Measurement is the process of assigning numbers to variables of individual population units.

  1. A) True B) False

23)                 

 

 

24) A census is feasible when the population of interest is  small.

  1. A) True B) False

24)                 

 

 

25) The process of using information from a sample to make generalizations about the larger population is called statistical inference.

  1. A) True B) False

25)                 

26) A measure of reliability is an important element of a descriptive statistical problem.

  1. A) True B) False

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) When we study a process, what is generally the focus?

  1. A) the black box B) the subprocesses
  2. C) the input D) the output

1)                    

 

 

2) In the context of processes, what is a sample?

  1. A) any set of output B) any set of input
  2. C) any subset of the population D) any set of subprocesses

2)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

3) What do we call a process whose operations are unknown or unspecified?                                     3)                                    

 

 

4) A chain of coffee shops has 45 stores in one metropolitan area. For liability reasons, the chain is interested in the average temperature of hot drinks served at the stores. Three stores were chosen and the temperature of every fifth hot drink served at each of these stores was recorded during a two-week period. At the end of the two-week period, the temperatures of 10,571 hot drinks had been recorded.

 

  1. Identify the process of interest. b.    Identify the variable of interest. c.    Describe the sample.
  2. Describe the inference of interest.

4)                                    

 

 

5) A department store receives customer orders through its call center and website. These orders as well as any special orders received in the stores are forwarded to a distribution center where workers pull the items on the orders from inventory, pack the items, and prepare the necessary paperwork for the shipping company that will pick the orders up and deliver them to the customers. In order to monitor the subprocess of pulling the items from inventory, every 15 minutes one order is checked to determine whether the worker has pulled the correct item.

 

  1. Identify the process of interest. b.    Identify the variable of interest. c.    Describe the sample.
  2. Describe the inference of interest.

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) The amount of television viewed by today’s youth is of primary concern to Parents Against

Watching Television (PAWT). 250 parents of elementary school -aged children were asked to estimate the number of hours per week that their child watches television. Identify the type of data collected by PAWT.

  1. A) qualitative B) quantitative

1)                    

 

 

2) The manager of a car dealership records the colors of automobiles on a used car lot. Identify the type of data collected.

  1. A) quantitative B) qualitative

2)                    

 

 

3) A postal worker counts the number of complaint letters received by the United States Postal

Service in a given day. Identify the type of data collected.

  1. A) quantitative B) qualitative

3)                    

 

 

4) An usher records the number of unoccupied seats in a movie theater during each viewing of a film.

Identify the type of data collected.

  1. A) quantitative B) qualitative

4)                    

 

 

5) A fan observes the numbers on the shirts of a girl’s soccer team. Identify the type of data collected.

  1. A) qualitative B) quantitative

5)                    

 

 

6) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. What type of variable is the administration interested in collecting?

  1. A) quantitative data B) qualitative data

6)                    

 

 

7) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. What type of variable is being collected?

  1. A) quantitative data B) qualitative data

7)                    

 

 

8) A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. What type of variable is being collected?

  1. A) qualitative data B) quantitative data

8)                    

 

 

9) Which data about paintings would not be qualitative?

  1. A) the artist B) the value C) the style                             D) the theme

9)                    

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

10) Gender is one variable of interest in a study of the effectiveness of a new medication. For data entry purposes, the researcher conducting the study assigns 1 for Male and 2 for Female. Is the gender data quantitative or qualitative?

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Solve the problem.

1) The amount of television viewed by today’s youth is of primary concern to Parents Against

Watching Television (PAWT). 250 parents of elementary school -aged children were asked to estimate the number of hours per week that their child watches television. Identify the type of data collected by PAWT.

  1. A) qualitative B) quantitative

1)                    

 

 

 

 

2) The manager of a car dealership records the colors of automobiles on a used car lot. Identify the type of data collected.

  1. A) quantitative B) qualitative

2)                    

 

 

 

 

3) A postal worker counts the number of complaint letters received by the United States Postal

Service in a given day. Identify the type of data collected.

  1. A) quantitative B) qualitative

3)                    

 

 

 

 

4) An usher records the number of unoccupied seats in a movie theater during each viewing of a film.

Identify the type of data collected.

  1. A) quantitative B) qualitative

4)                    

 

 

 

 

5) A fan observes the numbers on the shirts of a girl’s soccer team. Identify the type of data collected.

  1. A) qualitative B) quantitative

5)                    

 

 

 

 

6) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. What type of variable is the administration interested in collecting?

  1. A) quantitative data B) qualitative data

6)                    

 

 

 

 

7) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. What type of variable is being collected?

  1. A) quantitative data B) qualitative data

7)                    

 

 

 

 

8) A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. What type of variable is being collected?

  1. A) qualitative data B) quantitative data

8)                    

 

 

 

 

9) Which data about paintings would not be qualitative?

  1. A) the artist B) the value C) the style                             D) the theme

9)                    

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

10) Gender is one variable of interest in a study of the effectiveness of a new medication. For data entry purposes, the researcher conducting the study assigns 1 for Male and 2 for Female. Is the gender data quantitative or qualitative?

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

Solve the problem.

1) Define statistical thinking.                                                                                                                                 1)                                    

 

 

2) Give an example of unethical statistical practice.                                                                                      2)                                    

 

 

 

3) A health food company has the following statement on their new product packaging: “Prevents all types of cancer!” (Fact: Past studies have shown that some ingredients in the new product have been know to possibly reduce the risk of many types of cancer). Discuss why it is unethical to make this statement.

3)                                    

 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

4) A researcher studying malnutrition among children in a developing country collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than

the actual weight. Which statement best describes this situation?

  1. A) Measurement error has occurred, but the researcher is not guilty of unethical statistical practice.
  2. B) Measurement error has not occurred, but the researcher is guilty of unethical statistical practice.
  3. C) Measurement error has not occurred, and the researcher is not guilty of unethical statistical practice.
  4. D) Measurement error has occurred, and the researcher is guilty of unethical statistical

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) In an eye color study, 25 out of 50 people in the sample had brown eyes.  In this situation, what

does the number .50 represent?

  1. A) a class B) a class frequency
  2. C) a class percentage D) a class relative frequency

1)                    

 

 

2) What class percentage corresponds to a class relative frequency of .37?

  1. A) 37% B) 63% C) .63%                                   D) .37%

2)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

3) A sample of 100 e-mail users were asked whether their primary e-mail account was a free account, an institutional (school or work) account, or an account that they pay for personally.  Identify the classes for the resulting data.

3)                                    

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

4) What number is missing from the table?

4)                    

 

Grades

on Test

 

Frequency

Relative

Frequency

A 6 .24
B 7
C 9 .36
D 2 .08
F 1 .04

 

  1. A) .72 B) .28 C) .07                                       D) .70

 

 

5) What number is missing from the table?

5)                    

 

Year in

College

 

Frequency

Relative

Frequency

Freshman 600 .30
Sophomore 560 .28
Junior .22
Senior 400 .20

 

  1. A) 440 B) 480 C) 220                                      D) 520

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

6) Complete the frequency table for the data shown below.

6)                                    

 

green blue brown orange blue
brown orange blue red green
blue brown green red brown
blue brown blue blue red

 

Color Frequency
Green
Blue
Brown
Orange

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

7) A frequency table displays the proportion of observations falling into each class.

  1. A) True B) False

7)                    

 

 

Solve the problem.

8) 260 randomly sampled college students were asked, among other things, to state their year in

school (freshman, sophomore, junior, or senior). The responses are shown in the bar graph below.

How many of the students who responded would be classified as upperclassmen (e.g., juniors or seniors)?

  1. A) Approximately 100 B) Approximately 10
  2. C) Approximately 25 D) Approximately 125

8)                    

9)

The manager of a store conducted a customer survey to determine why customers shopped at the store. The results are shown in the figure. What proportion of customers responded that merchandise was the reason they shopped at the store?

9)                    

  1. A) 30 B) 3

7

  1. C) 2

7

  1. D) 1

2

 

 

10)

 

The bar graph shows the political affiliation of 1000 registered U.S. voters. What percentage of the voters belonged to one of the traditional two parties (Democratic or Republican)?

  1. A) 75% B) 25% C) 35%                                    D) 40%

10)                 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

11) The data below show the types of medals won by athletes representing the United States in the Winter Olympics.

11)                                 

 

gold gold silver gold bronze silver silver
bronze gold silver silver bronze silver gold
gold silver silver bronze bronze gold silver
gold gold bronze bronze

 

  1. Construct a frequency table for the data.
  2. Construct a relative frequency table for the data.
  3. Construct a frequency bar graph for the data.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

12) The bars in a bar graph can be arranged by height in ascending order from left to right.

  1. A) True B) False

12)                 

 

 

13) Either vertical or horizontal bars can be used when constructing a bar graph.

  1. A) True B) False

13)                 

 

 

Solve the problem.

14)

 

The pie chart shows the classifications of students in a statistics class.

 

What percentage of the class consists of freshman, sophomores, and juniors?

  1. A) 54% B) 14% C) 44%                                    D) 86%

14)                 

15) One of the questions posed to a sample of 286 incoming freshmen at a large public university was, “Do you have any tattoos?” Their responses are shown below in the pie chart. Please note that the values shown represent the number of responses in each category.

Based on the responses shown in the pie chart, what percentage of the freshmen responded with

“Yes?”

  1. A) 4% B) 76 C) 26.6%                                 D) 76%

15)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

16) The table shows the number of each type of book found at an online auction site during a recent search.

16)                                 

 

Type of Book Number
Children’s 51,033
Fiction 141,114
Nonfiction 253,074
Educational 67,252

 

  1. Construct a relative frequency table for the book data. b.    Construct a pie chart for the book data.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

17) If 25% of your statistics class is sophomores, then in a pie chart representing classifications of the

students in your statistics class the slice assigned to sophomores is 90°.

  1. A) True B) False

17)                 

 

 

18) The slices of a pie chart must be arranged from largest to smallest in a clockwise direction.

  1. A) True B) False

18)                 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

Solve the problem.

19) What characteristic of a Pareto diagram distinguishes it from other bar graphs?                           19)                                 

 

 

20) The table shows the number of each type of car sold in June.

20)                                 

 

Car Number
compact 7,204
sedan 9,089
small SUV 20,418
large SUV 13,691
minivan 15,837
truck 15,350
Total 81,589

 

  1. Construct a relative frequency table for the car sales.
  2. Construct a Pareto diagram for the car sales using the class percentages as the heights

of the bars.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

21) Class relative frequencies must be used, rather than class frequencies or class percentages, when

constructing a Pareto diagram.

  1. A) True B) False

21)                 

 

 

22) A Pareto diagram is a pie chart where the slices are arranged from largest to smallest in a counterclockwise direction.

  1. A) True B) False

22)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

Solve the problem.

23) An annual survey sent to retail store managers contained the question “Did your store

suffer any losses due to employee theft?”  The responses are summarized in the table for

two years.  Compare the responses for the two years using side -by-side bar charts.  What inferences can be made from the charts?

23)                                 

 

Employee

Theft

Percentage

in year 1

Percentage

in year 2

Yes

No

Don’t know

 

Totals

34

51

15

 

100

23

68

9

 

100

 

 

 

1) D

2) A

3) free account, institutional account, account paid for personally

4) B

5) A

6)

 

Color Frequency
Green 3
Blue 7
Brown 5
Orange 2
Red 3

7) B

8) D

9) B

10) A

11) a.

 

Medal Frequency
Gold 9
Silver 9
Bronze 7

 

b.

 

Medal Relative

Frequency

Gold .36
Silver .36
Bronze .28

 

c.

 

12) A

13) A

14) D

15) C

 

 

 

16) a.

 

Type of Book Relative

Frequency

Children’s .10
Fiction .28
Nonfiction .49
Educational .13

 

b.

 

17) A

18) B

19) In a Pareto diagram, the bars are arranged by height in a descending order from left to right.

Exam

 

Name

 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Solve the problem.

1) The payroll amounts for all teams in an international hockey league are shown below using a

graphical technique from chapter 2 of the text.  How many of the hockey team payrolls exceeded

$20 million (Note: Assume that no payroll was exactly $20 million)?

 

  1. A) 8 teams B) 18 teams C) 10 teams        D) 23 teams

 

 

1)

 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

2) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics.

 

1              2              3              3              4              9              9              11   11

 

11   14   14  19   22   23   24   25   29

 

  1. Complete the class frequency table for the data.

 

2)

 

 

Total Medals      Frequency

1-5

6-10

11-15

16-20

21-25

26-30

 

  1. Using the classes from the frequency table, construct a histogram for the data.

 

3) The total points scored by a basketball team for each game during its last season have been summarized in the table below.

 

3)

 

 

Score     Frequency

41-60     3

61-80     8

81-100   12

101-120                7

 

  1. Explain why you cannot use the information in the table to construct a stem -and-leaf display for the data.
  2. Construct a histogram for the scores.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Answer the question True or False.

4) All class intervals in a histogram have the same width.

  1. A) True B) False

 

 

4)

 

 

 

 

5) A histogram can be constructed using either class frequencies or class relative frequencies as the heights of the bars.

  1. A) True B) False

 

5)

 

 

 

 

6) The bars in a histogram should be arranged by height in descending order from left to right.

  1. A) True B) False

 

6)

 

 

 

 

Solve the problem.

7) A survey was conducted to determine how people feel about the quality of programming available

on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100

(extremely good quality). The stem-and-leaf display of the data is shown below.

 

Stem Leaf

3 1  6

4 0  3  4  7  8  9  9  9

5 0  1  1  2  3  4  5

6 1  2  5  6  6

7 1  4

8

9 5

 

 

7)

 

 

What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)?

  1. A) 20% B) 4% C) 1% D) 5%

 

8) 252 randomly sampled college students were asked, among other things, to estimate their college grade point average (GPA). The responses are shown in the stem -and-leaf plot shown below. Notice that a GPA of 3.65 would be indicated with a stem of 36 and a leaf of 5 in the plot. How many of the students who responded had GPA’s that exceeded 3.55?

 

Stem and Leaf Plot of GPA

 

Leaf Digit Unit = 0.01       Minimum  1.9900

19  9  represents 1.99     Median   3.1050

Maximum  4.0000

 

8)

 

Stem     Leaves

1              19           9

5              20           0668

6              21           0

11           22           05567

15           23           0113

20           24           00005

33           25           0000000000067

46           26           0000005577789

61           27           000000134455578

79           28           000000000144667799

88           29           002356777

116         30           0000000000000000000011344559

(19          ) 31         0000000000112235666

117         32           0000000000000000345568

95           33           000000000025557

80           34           0000000000000000333444566677889

49           35           000003355566677899

31           36           000005

25           37           022235588899

13           38           00002579

5              39           7

4              40           0000

 

252 cases included

 

  1. A) 49 B) 39 C) 31      D) 19

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

9) The scores for a statistics test are as follows:

 

87   76   92   77   92   96   88   85   66   89

79   96   50   98   83   88   82   51   10   69

 

Create a stem-and-leaf display for the data.

 

9)

 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Answer the question True or False.

10) For large data sets, a stem-and-leaf display is a better choice than a histogram.

  1. A) True B) False

 

 

10)

 

Solve the problem.

11) A dot plot of the speeds of a sample of 50 cars passing a policeman with a radar gun is shown

below.

 

 

 

What proportion of the motorists were driving above the posted speed limit of 55 miles per hour?

  1. A) 0.50 B) 7 C) 0.14 D) 0.64

 

 

11)

 

 

 

 

12) Which of the graphical techniques below can be used to summarize qualitative data?

  1. A) box plot B) stem-and-leaf plot
  2. C) bar graph D) dot plot

 

12)

 

 

 

 

13) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 90 students and recorded how long it took each of them to find a parking spot. Which of the following types of graphs should not be used to display information concerning the students parking times?

  1. A) pie chart B) box plot
  2. C) stem-and-leaf display D) histogram

 

13)

 

 

 

 

14) Fill in the blank. One advantage of the            is that the actual data values are retained in the graphical summarization of the data.

  1. A) pie chart B) stem-and-leaf plot C) histogram

 

14)

 

 

 

 

1) D

2) a.

 

Total Medals      Frequency

1-5          5

6-10       2

11-15     5

16-20     1

21-25     4

26-30     1

 

b.

 

3) a.       The exact scores would be needed to construct a stem-and-leaf display but  the exact scores are not available in the table given.

 

b.

 

4) A

5) A

6) B

7) B

8) B MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) The amount spent on textbooks for the fall term was recorded for a sample of five university

students – $400, $350, $600, $525, and $450. Calculate the value of the sample mean for the data.

1)                    

A) $400 B) $465 C) $450 D) $600

 

2) The amount spent on textbooks for the fall term was recorded for a sample of five university students – $400, $350, $600, $525, and $450. Calculate the value of the sample median for the data.

2)                    

A) $450 B) $600 C) $400 D) $465

 

3) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows:

3)                    

 

72 77 70 80 90
78 65 93 69 94
73 96 80 66 85
67 72 85 74 77
64 91 79 68 86

 

Find the median of the observations.

A) 77.5 B) 74 C) 78 D) 77

 

4) The scores for a statistics test are as follows:

 

75   76   62   77   70   92   61   85   95   89

79   67   50   60   85   65   85   73   18   82

 

Compute the mean score.

  1. A) 25 B) 75 C) 72.30                                  D) 75.50

4)                    

 

 

5) A shoe retailer keeps track of all types of information about sales of newly released shoe styles.

One newly released style was marketed to tall people. Listed below are the shoe sizes of 12

randomly selected customers who purchased the new style. Find the mode of the shoe sizes.

5)                    

 

9 1               11               12             11 1

2                                                       2

8 1             10 1

2                  2

8                11

10               11             9 1

2

  1. A) 10 1

4

10

 

  1. B) 9 1

2

 

 

  1. C) 11 D) 10 1

2

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

6) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed:

6)                                    

 

Company A $71 Company F $25.9
Company B 63.7 Company G 24.6
Company C 54.5 Company H 23.1
Company D 54.1 Company I 23.6
Company E 28.5 Company J 19.8

 

Calculate the mean and median for the data.

 

 

7) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the mean, median, and mode of the numbers of medals won by these countries.

7)                                    

 

1 2 3 3 4 9 9 11 11
11 14 14 19 22 23 24 25 29

 

 

8) Calculate the mean of a sample for which ∑x  =  196 and n = 8.                                                           8)                                    

 

 

9) The calculator screens summarize a data set.

  1. How many data items are in the set?
  2. What is the sum of the data?
  3. Identify the mean, median, and mode, if possible.

9)                                    

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

10) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 96 miles per hour. Suppose that the statistician indicated that the serve speed distribution was skewed to the left. Which of the following values is most likely the value of the median serve speed?

  1. A) 101 mph B) 91 mph C) 96 mph                              D) 86 mph

10)                 

11) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the mean is correct?

  1. A) The average of the textbook costs sampled was $500
  2. B) The most frequently occurring textbook cost in the sample was $500
  3. C) 50% of the students sampled had textbook costs that were less than $500
  4. D) 50% of the students sampled had textbook costs equal to $500

11)                 

 

 

12) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct?

  1. A) The average of the textbook costs sampled was $425
  2. B) 50% of the students sampled had textbook costs equal to $425
  3. C) 50% of the students sampled had textbook costs that were less than $425
  4. D) The most frequently occurring textbook cost in the sample was $425

12)                 

 

 

13) During one recent year, U.S. consumers redeemed 6.52 billion manufacturers’ coupons and saved themselves $2.16 billion. Calculate and interpret the mean savings per coupon.

  1. A) Half of all coupons were worth more than 9 cents in savings.
  2. B) The average savings was $0.33 per
  3. C) Half of all coupons were worth more than $0.33 in
  4. D) The average savings was 9 cents per coupon.

13)                 

 

 

14) The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5.

14)                 

 

Year 1 Year 5
N 51 51
MEAN 28.94 26.53
MEDIAN 27.78 25.64

 

Interpret the year 5 median dropout rate of 25.64.

  1. A) Half of the 51 states had a dropout rate below 64%.
  2. B) Half of the 51 states had a dropout rate of 64%.
  3. C) Most of the 51 states had a dropout rate close to 64%.
  4. D) The most frequently observed dropout rate of the 51 states was 64%.

15)

 

 

For the distribution drawn here, identify the mean, median, and mode.

  1. A) A = mode, B = median, C = mean B) A = mode, B = mean, C = median
  2. C) A = median, B = mode, C = mean D) A = mean, B = mode, C = median

15)                 

 

 

16) In a distribution that is skewed to the right, what is the relationship of the mean, median, and mode?

  1. A) mode > mean > median B) median > mean > mode
  2. C) mean > median > mode D) mode > median > mode

16)                 

 

 

17) Many firms use on-the-job training to teach their employees computer programming. Suppose

you work in the personnel department of a firm that just finished training a group of its employees

to program, and you have been requested to review the performance of one of the trainees on the

final test that was given to all trainees. The mean of the test scores is 70. Additional information indicated that the median of the test scores was 80. What type of distribution most likely describes the shape of the test scores?

  1. A) unable to determine with the information given
  2. B) symmetric
  3. C) skewed to the left
  4. D) skewed to the right

17)                 

 

 

18) A shoe company reports the mode for the shoe sizes of men’s shoes is 12. Interpret this result.

  1. A) Half of the shoes sold to men are larger than a size 12
  2. B) The most frequently occurring shoe size for men is size 12
  3. C) Half of all men’s shoe sizes are size 12
  4. D) Most men have shoe sizes between 11 and

18)                 

 

 

19) Which of the following is not a measure of central tendency?

  1. A) range B) mode C) mean                                  D) median

19)                 

 

 

20) The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?

  1. A) median B) mean C) mode                                  D) range

20)                 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

21) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 190 students and recorded how long it took each of them to find a parking spot. The times had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 190 times collected.

21)                                 

 

 

22) The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5.

22)                                 

 

Year 1 Year 5
N 51 51
MEAN 28.22 26.56
MEDIAN 27.53 25.18

 

Use the information to determine the shape of the distributions of the high school dropout rates in year 1 and year 5.

 

 

23) The total points scored by a basketball team for each game during its last season have been summarized in the table below. Identify the modal class of the distribution of scores.

23)                                 

 

Score Frequency
41-60 3
61-80 8
81-100 12
101-120 7

 

 

 

24) The calculator screens summarize a data set.

  1. Identify the mean and the median.
  2. Based only on the mean and the median, do you expect that the data set is skewed to the right, symmetric, or skewed to the left? Explain.

24)                                 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

25) The mean and the median are useful measures of central tendency for both qualitative and

quantitative data.

  1. A) True B) False

25)                 

26) In a symmetric and mound shaped distribution, we expect the values of the mean, median, and mode to differ greatly from one another.

  1. A) True B) False

26)                 

 

 

27) In symmetric distributions, the mean and the median will be approximately equal.

  1. A) True B) False

27)                 

 

 

28) In skewed distributions, the mean is the best measure of the center of the distribution since it is least affected by extreme observations.

  1. A) True B) False

28)                 

 

 

29) In practice, the population mean μ is used to estimate the sample mean x.

  1. A) True B) False

29)                 

 

 

30) In general, the sample mean is a better estimator of the population mean for larger sample sizes.

  1. A) True B) False

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) Each year advertisers spend billions of dollars purchasing commercial time on network television.

In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed:

1)                    

 

Company A $70.7 Company F $24.8
Company B 63.9 Company G 24
Company C 55.7 Company H 22.7
Company D 54.2 Company I 23.2
Company E 30.3 Company J 20.1

 

Calculate the sample variance.

  1. A) 965 B) 1864.521 C) 2080.829                           D) 3763.035

 

 

2) Calculate the range of the following data set:

 

8, 8, 4, 1, 9, 12, 8, 5, 5

  1. A) 13 B) 12 C) 11                                        D) 1

2)                    

 

 

3) The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places.

 

195, 100, 165, 130, 145

  1. A) 1702 B) 35.8120 C) 130.01                                D) 168.0982

3)                    

 

 

4) The amount spent on textbooks for the fall term was recorded for a sample of five university students – $400, $350, $600, $525, and $450. Calculate the value of the sample range for the data.

  1. A) $450 B) $98.75 C) $250                                   D) $99.37

4)                    

 

 

5) The amount spent on textbooks for the fall term was recorded for a sample of five university students – $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data.

  1. A) $450 B) $99.37 C) $250                                   D) $98.75

5)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

6) The ages of five randomly chosen professors are 58, 61, 62, 69, and 44. Calculate the sample variance of these ages.

6)                                    

7) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries.

7)                                    

 

1 2 3 3 4 9 9 11 11
11 14 14 19 22 23 24 25 29

 

 

8) The calculator screens summarize a data set.

  1. Identify the smallest measurement in the data set. b. Identify the largest measurement in the data set.
  2. Calculate the range of the data set.

8)                                    

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

9) Calculate the variance of a sample for which n = 5, ∑x2 = 1320, ∑x = 80.

  1. A) 00 B) 8.00 C) 3.16                                     D) 326.00

 

10) Calculate the standard deviation of a sample for which n = 6, ∑x 2 = 830, ∑x = 60.

  1. A) 00 B) 6.19 C) 6.78                                     D) 46.00

 

 

9)                    

 

 

 

10)                 

 

 

11) Compute s2 and s for the data set: -2, 1, -4, -2, 1, -2

  1. A) 87; 1.97 B) 2.87; 1.69 C) 3.44; 1.85                          D) 11.8; 3.44

11)                 

 

 

12) Compute s2 and s for the data set:  1 ,  7 ,  1 , 3 ,  1 , 1 .

12)                 

10   10

10   5

10   5

  1. A) 617; 0.786 B) 0.045; 0.213 C) 7.6; 2.757                          D) 0.076; 0.276

 

 

13) The range of scores on a statistics test was 42.  The lowest score was 57.  What was the highest score?

  1. A) 99 B) 5
  2. C) 78 D) cannot be determined

13)                 

 

 

14) The temperature fluctuated between a low of 73°F and a high of 89°F.  Which of the following could be calculated using just this information?

  1. A) range B) standard deviation
  2. C) variance D) median

14)                 

 

 

15) Which of the following is a measure of the variability of a distribution?

  1. A) range B) median C) sample size                     D) skewness

15)                 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

16) Various state and national automobile associations regularly survey gasoline stations to determine the current retail price of gasoline. Suppose one such national association contacts 200 stations in the United States to determine the price of regular unleaded gasoline at each station. In the context of this problem, define the following descriptive

measures:  μ, σ, x, s.

16)                                 

 

 

17) Given the sample variance of a distribution, explain how to find the standard deviation.          17)                                 

 

 

18) Which is expressed in the same units as the original data, the variance or the standard deviation?

18)                                 

 

 

19) Which measures variability about the mean, the range or the standard deviation?                       19)                                 

 

 

20) For a given data set, which is typically greater, the range or the standard deviation?                   20)                                 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

21) The total points scored by a basketball team for each game during its last season have been summarized in the table below. Which statement following the table must be true?

21)                 

 

Score Frequency
41-60 3
61-80 8
81-100 12
101-120 7

 

  1. A) The range is B) The range is at least 41 but at most 120. C) The range is at least 41 but at most 79.                    D) The range is at least 81 but at most 100.

 

 

22) Which number on the screen below is the sample standard deviation of the data?

 

 

  1. A) 408 B) 8 C) 2.67                                     D) 2.82

22)                 

 

 

Answer the question True or False.

23) The range is an insensitive measure of data variation for large data sets because two data sets can

have the same range but be vastly different with respect to data variation.

  1. A) True B) False

23)                 

24) For any quantitative data set, ∑(x x ) = 0.

  1. A) True B) False

24)                 

 

 

25) The sample variance and standard deviation can be calculated using only the sum of the data, ∑x , and the sample size, n.

  1. A) True B) False

25)                 

 

 

26) The sample variance is always greater than the sample standard deviation.

  1. A) True B) False

26)                 

 

 

27) A larger standard deviation means greater variability in the data.

  1. A) True B) False

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Solve the problem.

1) The mean x of a data set is 36.71, and the sample standard deviation s is 3.22.  Find the interval representing measurements within one standard deviation of the mean.

  1. A) (35.71, 37.71) B) (27.05, 46.37) C) (33.49, 39.93)                D) (30.27, 43.15)

 

 

1)

 

 

 

 

2) The following is a list of 25 measurements:

 

2)

 

 

12           18           14           17           19           16           14           18           15           17           11

13           14           11           16           18           15           13           17           15           14           19

12           16           17

 

How many of the measurements fall within one standard deviation of the mean?

  1. A) 18 B) 13 C) 25      D) 16

 

 

 

3) A standardized test has a mean score of 500 points with a standard deviation of 100 points.  Five students’ scores are shown below.

 

Adam: 575           Beth: 690             Carlos: 750    Doug: 280 Ella: 440

 

Which of the students have scores within two standard deviations of the mean?

  1. A) Adam, Beth B) Adam, Beth, Carlos, Ella
  2. C) Carlos, Doug D) Adam, Beth, Ella

 

3)

 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

4) The mean x of a data set is 18, and the sample standard deviation s is 2. Explain what the interval (12, 24) represents.

 

4)

 

 

 

 

5) The calculator screens summarize a data set.

 

  1. Identify the mean and the sample standard deviation. Round to one place after the decimal, where  necessary.
  2. Find the interval that corresponds to measurements within two standard deviations of the mean.

 

5)

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

6) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician

also gave us the information that the distribution of serve speeds was mound -shaped and symmetric.  What percentage of the player’s serves were between 115 mph and 145 mph?

  1. A) at most 13.5% B) approximately 16%
  2. C) at most 2.5% D) at most 34%

 

6)

 

 

 

 

7) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 97 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player’s serves was between 110 mph and

136 mph?

  1. A) 0.1585 B) 0.997 C) 136    D) 0.317

 

7)

 

 

 

 

8) The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming the distribution of commuting times is known to be moundshaped and symmetric, what percentage of these commuting times are between 50 and 110 minutes?

  1. A) approximately 97.5% B) approximately 95% C) approximately 81.5% D) approximately 68%

 

8)

 

 

 

 

9) The amount of television viewed by today’s youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school -aged children were asked to estimate the number of hours per week that their child watches television. The mean and the standard deviation for their responses were 17 and 3, respectively. PAWT constructed a

stem-and-leaf display for the data that showed that the distribution of times was a symmetric, mound-shaped distribution. Give an interval where you believe approximately 95% of the television viewing times fell in the distribution.

  1. A) between 8 and 26 hours per week
  2. B) less than 14 and more than 20 hours per week
  3. C) less than 23
  4. D) between 11 and 23 hours per week

 

9)

 

 

 

 

10) A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows:

 

68   73   66   76   86   74   61   89   65   90   69   92   76

62   81   63   68   81   70   73   60   87   75   64   82

 

Suppose the mean and standard deviation are 74.04 and 9.75, respectively. If we assume that the distribution of ages is mound-shaped and symmetric, what percentage of the respondents will be between 64.29 and 93.54 years old?

  1. A) approximately 95% B) approximately 68%
  2. C) approximately 84% D) approximately 81.5%

 

10)

 

11) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound -shaped and symmetric, with a mean of 85 jobs and a standard deviation of 5. Where do we expect approximately 95% of the distribution to fall?

  1. A) between 80 and 90 jobs per day B) between 70 and 100 jobs per day
  2. C) between 75 and 95 jobs per day D) between 95 and 100 jobs per day

 

11)

 

 

 

 

12) A study was designed to investigate the effects of two variables  (1) a student’s level of mathematical anxiety and (2) teaching method  on a student’s achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 350 with a standard deviation of 40 on a standardized test. Assuming a mound-shaped and symmetric distribution, what percentage of scores exceeded 270?

  1. A) approximately 84% B) approximately 100%
  2. C) approximately 97.5% D) approximately 95%

 

12)

 

 

 

 

13) A study was designed to investigate the effects of two variables  (1) a student’s level of mathematical anxiety and (2) teaching method  on a student’s achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 440 with a standard deviation of 50 on a standardized test. Assuming a mound-shaped and symmetric distribution, in what range would approximately 68% of the students score?

  1. A) above 490 B) below 390 and above 490
  2. C) below 490 D) between 390 and 490

 

13)

 

 

 

 

14) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $104 and a standard deviation of

$10. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $94?

  1. A) approximately 34% B) approximately 84% C) approximately 95%      D) approximately 16%

 

14)

 

 

 

 

15) Many firms use on-the-job training to teach their employees computer programming. Suppose

you work in the personnel department of a firm that just finished training a group of its employees

to program, and you have been requested to review the performance of one of the trainees on the

final test that was given to all trainees. The mean and standard deviation of the test scores are 84

and 5, respectively, and the distribution of scores is mound -shaped and symmetric. What percentage of test-takers scored better than a trainee who scored 69?

  1. A) approximately 100% B) approximately 95%
  2. C) approximately 84% D) approximately 97.5%

 

15)

 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

16) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 98 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. Find the percentage of serves that were hit faster than 72 mph.

 

16)

 

17) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound -shaped and symmetric, with a mean of 93 jobs and a standard deviation of 8. On what percentage of days do the number of jobs submitted exceed 101?

 

17)

 

 

 

 

18) By law, a box of cereal labeled as containing 24 ounces must contain at least 24 ounces of cereal. The machine filling the boxes produces a distribution of fill weights that is

mound-shaped and symmetric, with a mean equal to the setting on the machine and with a standard deviation equal to 0.02 ounce. To ensure that most of the boxes contain at least

24 ounces, the machine is set so that the mean fill per box is 24.06 ounces. What percentage of the boxes do, in fact, contain at least 24 ounces?

 

18)

 

 

 

 

19) Many firms use on-the-job training to teach their employees computer programming.

Suppose you work in the personnel department of a firm that just finished training a

group of its employees to program, and you have been requested to review the

performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 76 and 4, respectively, and the distribution of scores is mound-shaped and symmetric. If a firm wanted to give the best 2.5% of the trainees a big promotion, what test score would be used to identify the trainees in question?

 

19)

 

 

 

 

20) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9.

 

20)

 

 

39           51           59           63           66           68           68           69           70           71

71           71           73           74           76           76           76           77           78           79

79           79           79           80           80           82           83           83           83           85

85           86           86           88           88           88           88           89           89           89

90           90           91           91           92           95           96           97           97           98

 

What percentage of the scores lies within one standard deviation of the mean? two standard deviations of the mean? three standard deviations of the mean? Based on these percentages, do you believe that the distribution of scores is mound -shaped and symmetric? Explain.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

21) The distribution of scores on a test is mound -shaped and symmetric with a mean score of 78. If

68% of the scores fall between 72 and 84, which of the following is most likely to be the standard

deviation of the distribution?

  1. A) 6 B) 3 C) 12      D) 2

 

21)

 

 

 

 

22) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, what percentage of the player’s serve speeds are less than 70 mph?

  1. A) at most 25% B) at most 11%
  2. C) approximately 5% D) at most 12.5%
  3. E) approximately 2.5%

 

22)

 

23) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament.  The statistician reported that the mean serve speed of a particular player was 105 miles per hour (mph) and the standard deviation of the serve speeds was 9 mph.  If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player’s serves.

  1. A) 78 mph to 132 mph B) 87 mph to 123 mph
  2. C) 132 mph to 159 mph D) 69 mph to 141 mph

 

23)

 

 

 

 

24) The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes?

  1. A) at least 95% B) at least 89% C) at least 0% D) at least 75%

 

24)

 

 

 

 

25) By law, a box of cereal labeled as containing 36 ounces must contain at least 36 ounces of cereal.

The machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.02 ounce. To ensure that most of the boxes contain at least 36 ounces, the machine is set so that the mean fill per box is 36.06 ounces. Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 36 ounces.

  1. A) The proportion is at most 5.5%. B) The proportion is at least 89%.
  2. C) The proportion is at most 11%. D) The proportion is less than 2.5%.

 

25)

 

 

 

 

26) A study was designed to investigate the effects of two variables  (1) a student’s level of mathematical anxiety and (2) teaching method  on a student’s achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 470 with a standard deviation of 20 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 430 and 510?

  1. A) approximately 68% B) approximately 95% C) at least 75%     D) at least 89%

 

26)

 

 

 

 

27) A study was designed to investigate the effects of two variables  (1) a student’s level of mathematical anxiety and (2) teaching method  on a student’s achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 390 with a standard deviation of 30 on a standardized test. Assuming a non -mound-shaped distribution, what percentage of the students scored over 480?

  1. A) approximately 2.5% B) at most 11%
  2. C) at least 89% D) at most 5.5%

 

27)

 

 

 

 

28) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $90 and a standard deviation of

$15. If nothing is known about the shape of the distribution, what percentage of homes will have a

monthly utility bill of less than $60?

  1. A) at least 75% B) at most 11.1% C) at most 25% D) at least 88.9%

 

28)

 

29) Many firms use on-the-job training to teach their employees computer programming. Suppose

you work in the personnel department of a firm that just finished training a group of its employees

to program, and you have been requested to review the performance of one of the trainees on the

final test that was given to all trainees. The mean and standard deviation of the test scores are 82 and 5, respectively. Assuming nothing is known about the distribution, what percentage of

test-takers scored above 92?

  1. A) approximately 2.5% B) at least 75%
  2. C) approximately 97.5% D) at most 25%

 

29)

 

 

 

 

30) If nothing is known about the shape of a distribution, what percentage of the observations fall within 2 standard deviations of the mean?

  1. A) at least 75% B) approximately 95% C) approximately 5% D) at most 25%

 

30)

 

 

 

 

31) Fill in the blank.         gives us a method of interpreting the standard deviation of any data set, regardless of the shape of the distribution.

  1. A) The Empirical Rule B) Chebyshev’s Rule
  2. C) both A and B D) neither A nor B

 

31)

 

 

 

 

32) Fill in the blank.         is a method of interpreting the standard deviation of data that have a mound-shaped, symmetric distribution.

  1. A) The Empirical Rule B) Chebyshev’s Rule
  2. C) both A and B D) neither A nor B

 

32)

 

 

 

 

33) Given a data set, which of the following is most likely to be the percentage of data within three standard deviations of the mean?

  1. A) 85% B) 70% C) 95% D) 65%

 

33)

 

 

 

 

Answer the question True or False.

34) Both Chebyshev’s rule and the empirical rule guarantee that no data item will be more than four

standard deviations from the mean.

  1. A) True B) False

 

 

34)

 

 

 

 

35) Chebyshev’s rule applies to qualitative data sets, while the empirical rule applies to quantitative data sets.

  1. A) True B) False

 

35)

 

 

 

 

36) Chebyshev’s rule applies to large data sets, while the empirical rule applies to small data sets.

  1. A) True B) False

 

36)

 

 

 

 

37) Your teacher announces that the scores on a test have a mean of 83 points with a standard deviation of 4 points, so it is reasonable to expect that you scored at least 70 on the test.

  1. A) True B) False

 

37)

 

 

 

 

1) C

2) D

3) D

4) measurements within three standard deviations of the mean

5) a.  mean: x = 5.5; sample standard deviation: Sx ≈ 3.0 b.  (5.5 – 2 × 3.0, 5.5 + 2 × 3.0) = (-.5, 11.5)

6) B

7) A

8) C

9) D

10) D

11) C

12) C

13) D

14) B

15) A

16) We use the Empirical Rule to determine the percentage of serves with speeds faster than 72 mph. We do this by first finding the percentage of serves with speeds between 72 and 98 mph. The Empirical Rule states that approximately

34.0% (68%/2) fall between 72 and 98 mph. Because the distribution is symmetric about the mean speed of 98 mph, we know 50% of the serve speeds were faster than 98 mph. We add these findings together to determine that

34.0%  + 50% = 84.0% of the serves were hit faster than 72 mph.

17) The value 101 falls one standard deviation above the mean in the distribution. Using the Empirical Rule, 68% of the

days will have between 85 and 101 jobs submitted. Of the remaining 32% of the days, half, or 32%/2 = 16%, of the days will have more than 101 jobs submitted.

18) The value of 24 ounces falls three standard deviations below the mean. The Empirical Rule states that approximately all of the boxes will contain cereal amounts between 24.00 ounces and 24.12 ounces. Therefore, approximately 100% of the boxes contain at least 24 ounces.

19) The Empirical Rule states that 95% of the data will fall between 68 and 84. Because the distribution is symmetric, half

of the remaining 5%, or 2.5%, will have test scores above 84. Thus, 84 is the cutoff point that will identify the trainees who will receive the promotion.

20) 74% of the scores lie within one standard deviation of the mean, 96% within two standard deviations, and 98% within three standard deviations. These percentages are close to those given in the Empirical Rule, so the distribution is roughly mound-shaped and symmetric, though obviously skewed slightly to the left. MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) Many firms use on-the-job training to teach their employees computer programming. Suppose

you work in the personnel department of a firm that just finished training a group of its employees

to program, and you have been requested to review the performance of one of the trainees on the

final test that was given to all trainees. The mean and standard deviation of the test scores are 79

and 2, respectively, and the distribution of scores is mound -shaped and symmetric. Suppose the trainee in question received a score of 76. Compute the trainee’s z-score.

  1. A) z = -6 B) z = -3 C) z = -50                             D) z = 0.94

1)                    

 

 

2) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z -score for this student’s textbook expenditure.

  1. A) +3 B) +2 C) -2                                         D) -3

2)                    

 

 

3) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $100 and a standard deviation of

$14. Three solar homes reported monthly utility bills of $51, $48, and $56. Which of the following

statements is true?

  1. A) Homes using solar power always have lower utility bills than homes using only gas and electricity.
  2. B) Homes using solar power may have lower utility bills than homes using only gas and electricity.
  3. C) Homes using solar power may actually have higher utility bills than homes using only gas and
  4. D) The utility bills for homes using solar power are about the same as those for homes using only gas and

3)                    

 

 

4) A radio station claims that the amount of advertising each hour has a mean of 15 minutes and a standard deviation of 1.5 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 9 minutes. Calculate the z-score for this amount of advertising time.

  1. A) z = 00 B) z = 0.50 C) z = -9                                   D) z = -4.00

4)                    

 

 

5) On a given day, the price of a gallon of milk had a mean price of $2.16 with a standard deviation of

$0.07. A particular food store sold milk for $2.09/gallon. Interpret the z-score for this gas station.

  1. A) The milk price of this food store falls 7 standard deviations above the mean milk price of all

food stores.

  1. B) The milk price of this food store falls 7 standard deviations below the mean milk price of all food
  2. C) The milk price of this food store falls 1 standard deviation below the milk gas price of all food
  3. D) The milk price of this food store falls 1 standard deviation above the mean milk price of all food

5)                    

6) Which of the following is a measure of relative standing?

  1. A) mean B) variance C) pie chart                            D) z-score

6)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

7) A study was designed to investigate the effects of two variables  (1) a student’s level of mathematical anxiety and (2) teaching method  on a student’s achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 310 and a standard deviation of 50 on a standardized test. Find and interpret the z-score of a student who scored 490 on the standardized test.

7)                                    

 

 

8) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of

$124.00 and a standard deviation of $15.00. Assuming the distribution is mound-shaped and symmetric, would you expect to see a 3 -bedroom house using gas or electric energy with a monthly utility bill of $236.50? Explain.

8)                                    

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

9) Find the z-score for the value 88, when the mean is 70 and the standard deviation is 1.

  1. A) z = 24 B) z = 17.00 C) z = -1.24                             D) z = 18.00

9)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

10) Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a  mean of 69 with a standard deviation of  3.7. One student earned a 55 on the history test and a 70 on the physics test. Calculate the z-score for each test. On which test did the student perform better?

10)                                 

 

 

11) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9.

11)                                 

 

39 51 59 63 66 68 68 69 70 71
71 71 73 74 76 76 76 77 78 79
79 79 79 80 80 82 83 83 83 85
85 86 86 88 88 88 88 89 89 89
90 90 91 91 92 95 96 97 97 98

 

Find the z-scores for the highest and lowest exam scores.

 

 

12) The z-score for a value x is -2.5.  State whether the value of x lies above or below the mean and by how many standard deviations.

12)                                 

 

 

13) Suppose that 50 and 75 are two elements of a population data set and their z-scores are -3 and 2, respectively.  Find the mean and standard deviation.

13)                                 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

14) According to the empirical rule, z-scores of less than -3 or greater than 3 occur very infrequently for data from a mounded and symmetric distribution

  1. A) True B) False

14)                 

 

 

15) If a z-score is 0 or near 0, the measurement is located at or near the mean.

  1. A) True B) False

15)                 

 

 

16) If a sample has mean 0 and standard deviation 1, then for every measurement  x in the sample the

z-score of x is x itself.

  1. A) True B) False

16)                 

 

 

Solve the problem.

17) When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 87th percentile on the verbal part of the test and at the 14th percentile on the quantitative part. Interpret these results.

  1. A) This student performed better than 13% of the other test-takers on the verbal part and better than 14% on the quantitative
  2. B) This student performed better than 87% of the other test-takers on the verbal part and better than 86% on the quantitative
  3. C) This student performed better than 87% of the other test-takers on the verbal part and better than 14% on the quantitative
  4. D) This student performed better than 13% of the other test-takers on the verbal part and better than 86% on the quantitative

17)                 

 

 

18) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?

  1. A) 75% of the students sampled had textbook costs equal to $500. B) The average of the 500 textbook costs was $500.
  2. C) 75% of the students sampled had textbook costs that exceeded $500. D) 25% of the students sampled had textbook costs that exceeded $500.

18)                 

 

 

19) Summary information is given for the weights (in pounds) of 1000 randomly sampled tractor trailers.

19)                 

 

MIN: 3996 25%: 5596
MAX: 10,596 75%: 8596
AVE: 6996 Std. Dev.: 1400

 

Find the percentage of tractor trailers with weights between 5596 and 8596 pounds.

  1. A) 50% B) 25% C) 75%                                    D) 100%

 

 

20) The test scores of 30 students are listed below. Which number could be the 30th percentile?

20)                 

 

31 41 45 48 52 55 56 56 63 65
67 67 69 70 70 74 75 78 79 79
80 81 83 85 85 87 90 92 95 99
  1. A) 90 B) 56 C) 64                                        D) 67

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

21) A retail store’s customer satisfaction rating is at the 88 th percentile. What percentage of retail stores has higher customer satisfaction ratings than this store?

21)                                 

 

 

22) In a summary of recent real estate sales, the median home price is given as $325,000. What percentile corresponds to a home price of $325,000?

22)                                 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

23) The mean of a data set is at the 50 th percentile.

  1. A) True B) False

23)                 

 

 

24) Percentile rankings are of practical value only with large data sets.

  1. A) True B) False

24)                 

 

 

25) The process for finding a percentile is similar to the process for finding the median.

  1. A) True B) False

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits

during the tournament.  The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 8 mph.  Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player’s serve speeds?

 

Speeds: 72 mph, 108 mph, and 116 mph

 

  1. A) 72 and 108 are both outliers, but 116 is B) 72, 108, and 116 are all outliers.
  2. C) 72 is the only
  3. D) None of the three speeds is an

1)                    

 

 

2) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament.  The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player’s serve speeds?

 

Speeds:  50 mph, 80 mph, and 105 mph

  1. A) 50 and 80 are both outliers, 105 is B) None of the three speeds are outliers.
  2. C) 50, 80, and 105 are all D) 50 is the only outlier.

2)                    

 

 

3) The speeds of the fastballs thrown by major league baseball pitchers were measured by radar gun.

The mean speed was 86 miles per hour. The standard deviation of the speeds was 5 mph. Which of

the following speeds would be classified as an outlier?

  1. A) 94 mph B) 102 mph C) 76 mph                              D) 81 mph

3)                    

 

 

4) Which of the following statements concerning the box plot and z-score methods for detecting outliers is false?

  1. A) The box plot method is less affected by an extreme observation in the data
  2. B) The z-score method uses the mean and standard deviation as a basis for detecting C) The z-score method is less affected by an extreme observation in the data set.
  3. D) The box plot method uses the quartiles as a basis for detecting

4)                    

 

 

5) Which of the following statements could be an explanation for the presence of an outlier in the data?

  1. A) The measurement may be correct and from the same population as the rest but represents a rare Generally, we accept this explanation only after carefully ruling out all others.
  2. B) The measurement belongs to a population different from that from which the rest of the sample was
  3. C) The measurement is It may have been observed, recorded, or entered into the computer incorrectly.
  4. D) All of the above are explanations for

5)                    

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

6) A radio station claims that the amount of advertising each hour has an a mean of 17 minutes and a standard deviation of 2.5 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 11.75 minutes. Based on your observation, what would you infer about the radio station’s claim?

6)                                    

 

 

7) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9.

7)                                    

 

39 51 59 63 66 68 68 69 70 71
71 71 73 74 76 76 76 77 78 79
79 79 79 80 80 82 83 83 83 85
85 86 86 88 88 88 88 89 89 89
90 90 91 91 92 95 96 97 97 98

 

Use the z-score method to identify potential outliers among the scores.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

8) The z-score uses the quartiles to identify outliers in a data set.

  1. A) True B) False

8)                    

 

 

9) An outlier is defined as any observation that falls within the outer fences of a box plot.

  1. A) True B) False

9)                    

 

 

10) Box plots are used to detect outliers in qualitative data sets, while z-scores are used to detect outliers in quantitative data sets.

  1. A) True B) False

10)                 

 

 

11) An outlier in a data set may have a simple explanation such as a scale was not working properly or the researcher inverted the digits of a number when recording a measurement.

  1. A) True B) False

11)                 

 

 

12) An outlier may be caused by accidentally including the height of a six -year-old boy in a set of data representing the heights of 12-year-old boys.

  1. A) True B) False

12)                 

 

 

13) The outer fences of a box plot are three standard deviations from the mean.

  1. A) True B) False

13)                 

 

 

Solve the problem.

14) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits

during the tournament. The lower quartile of a particular player’s serve speeds was reported to be

99 mph. Which of the following interpretations of this information is correct?

  1. A) 75% of the player’s serves were hit at speeds less than 99
  2. B) 99 serves traveled faster than the lower C) 25% of the player’s serves were hit at 99 mph.
  3. D) 75% of the player’s serves were hit at speeds greater than 99

14)                 

15) A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows:

 

68   73   66   76   86   74   61   89   65   90   69   92   76

62   81   63   68   81   70   73   60   87   75   64   82

 

Find the upper quartile of the data.

  1. A) 73 B) 92 C) 5                                     D) 65.5

15)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

16) The amount of television viewed by today’s youth is of primary concern to Parents Against Watching Television (PAWT). Three hundred parents of elementary school -aged children were asked to estimate the number of hours per week that their child watches television. The upper quartile for the distribution was given as 20 hours. Interpret this value.

16)                                 

 

 

17) For a given data set, the lower quartile is 45, the median is 50, and the upper quartile is 57.

The minimum value in the data set is 32, and the maximum is 81.

 

  1. Find the interquartile range. b. Find the inner fences.
  2. Find the outer fences.
  3. Is either of the minimum or maximum values considered an outlier? Explain.

17)                                 

 

 

18) The calculator screens summarize a data set.

  1. Identify the lower and upper quartiles of the data set. b. Find the interquartile range.
  2. Is there reason to suspect that the data may contain an outlier? Explain.

18)                                 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

19) The box plot shown below displays the amount of soda that was poured by a filling machine into

12-ounce soda cans at a local bottling company.

 

 

Based on the box plot, what shape do you believe the distribution of the data to have?

  1. A) approximately symmetric B) skewed to the left
  2. C) skewed to the center D) skewed to the right

19)                 

 

 

20) The box plot shown below was constructed for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local soda bottling company.

We see that one soda can received 12.15 ounces of soda on the plot above. Based on the box plot presented, how would you classify this observation?

  1. A) expected observation B) it has a lot of soda
  2. C) suspect outlier D) highly suspect outlier

20)                 

21) The box plot shown below was constructed for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local soda bottling company.

We see that one soda can received 12.30 ounces of soda on the plot above. Based on the box plot presented, how would you classify this observation?

  1. A) highly suspect outlier B) it has a lot of soda
  2. C) suspect outlier D) expected observation

21)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

22) The following data represent the scores of 50 students on a statistics exam.

22)                                 

 

39 51 59 63 66 68 68 69 70 71
71 71 73 74 76 76 76 77 78 79
79 79 79 80 80 82 83 83 83 85
85 86 86 88 88 88 88 89 89 89
90 90 91 91 92 95 96 97 97 98

 

  1. Find the lower quartile, the upper quartile, and the median of the scores.
  2. Find the interquartile range of the data and use it to identify potential outliers.
  3. In a box plot for the data, which scores, if any, would be outside the outer fences? Which scores, if any, would be outside the inner fences but inside the outer fences?

 

 

23) Use a graphing calculator or software to construct a box plot for the following data set.

23)                                 

 

12 18 14      17      19      16      14      18      15      17      11
13 14 11      16      18      15      13      17      15      14      19
12 16 17

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Solve the problem.

1) A sample of professional golfers was taken and their driving distance (measured as the average

distance as their drive off the tee) and driving accuracy (measured as the percentage of fairways that their drives landed in) were recorded. A scatterplot of the variables is shown below.

 

What relationship do these two variables exhibit?

  1. A) They exhibit a positive linear relationship
  2. B) They exhibit a negative linear relationship
  3. C) They exhibit a curvillinear relationship
  4. D) They exhibit no relationship

 

 

1)

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

2) The data below represent the numbers of absences and the final grades of 15 randomly selected students from a statistics class. Construct a scattergram for the data. Do you detect a trend?

 

2)

 

 

Student                Number of Absences     Final Grade as a Percent

1              5              79

2              6              78

3              2              86

4              12           56

5              9              75

6              5              90

7              8              78

8              15           48

9              0              92

10           1              78

11           9              81

12           3              86

13           10           75

14           3              89

15           11           65

 

 

 

3) The scores of nine members of a women’s golf team in two rounds of tournament play are listed below.

 

3)

 

 

Player   1              2              3              4              5              6              7              8              9

Round 1

Round 2               85

90           90

87           87

85           78

84           92

86           85

78           79

77           93

91           86

82

 

Construct a scattergram for the data.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Answer the question True or False.

4) Scatterplots are useful for both qualitative and quantitative data.

  1. A) True B) False

 

 

4)

 

 

 

 

5) The scatterplot below shows a negative relationship between two variables.

 

  1. A) True B) False

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) Which of the following assignments of probabilities to the sample points A, B, and C is valid if A,

B, and C are the only sample points in the experiment?

1)                    

  1. A) P(A) = 1 , P(B) = 1 , P(C) = 1
  1. B) P(A) = 0, P(B) = 1 , P(C) = 8

5                 9                  6                                                                             9                  9

  1. C) P(A) = – 1 , P(B) = 1 , P(C) = 3
  1. D) P(A) = 1 , P(B) = 1 , P(C) =  1

4                  2                  4

10                 10                  10

 

 

2) If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table below.

2)                    

 

Sample Point A B C D .
Probability 1/7 1/7 1/7
A) 1

4

B) 4

7

C)  3

7

D) 1

7

 

 

3) A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:

3)                    

 

Color Number
Red 25
Brown 20
Green 20
Blue 15
Yellow 10
Orange 10

 

List the sample space for this problem.

  1. A) {0.25, 20, 0.20, 0.15, 0.10, 0.10} B) {Red}
  2. C) {Red, Brown, Green, Blue, Yellow, Orange} D) {25, 20, 20, 15, 10, 10}

4) A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:

4)                    

 

Color Number
Red 25
Brown 20
Green 20
Blue 15
Yellow 10
Orange 10

 

Find the probability that a randomly chosen piece of candy is not blue or red.

  1. A) 85 B) 0.15 C) 0.40                                     D) 0.60

 

 

5) Fill in the blank. A(n)              is a process that leads to a single outcome that cannot be predicted with certainty.

  1. A) sample space B) experiment C) event                                  D) sample point

5)                    

 

 

6) Fill in the blank. A(n)                      is the most basic outcome of an experiment.

  1. A) experiment B) sample space C) event                                  D) sample point

6)                    

 

 

7) Fill in the blank. The                      is the collection of all the sample points in an experiment.

  1. A) union B) Venn diagram C) event                                  D) sample space

7)                    

 

 

8) Fill in the blank. A(n)                      is a collection of sample points.

  1. A) event B) Venn diagram C) experiment                      D) sample space

8)                    

 

 

9) The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment?

  1. A) {nickel, dime} B) {HH, HT, TT}
  2. C) {0, 1, 2} D) {HH, HT, TH, TT}

9)                    

 

 

10) A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment?

  1. A) {80} B) {red, yellow, orange} C) {1/4, 5/16, 7/16}                                                                                                    D) {20, 25, 35}

10)                 

 

 

11) An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment?

  1. A) 2 B) 1 C) 6                                          D) 7

11)                 

 

 

12) Which number could be the probability of an event that occurs about as often as it does not occur?

  1. A) .51 B) 0 C) 1                                          D) -.51

12)                 

 

 

13) Which number could be the probability of an event that rarely occurs?

  1. A) -.01 B) .51 C) .99                                       D) .01

13)                 

 

 

14) Which number could be the probability of an event that is almost certain to occur?

  1. A) .51 B) .01 C) 01                                     D) .99

14)                 

15) Suppose that an experiment has five equally likely outcomes. What probability is assigned to each of the sample points?

  1. A) .2 B) 1 C) .5                                         D) .05

15)                 

 

 

16) An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.

  1. A) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B) {2, 4, 6, 8, 10}
  2. C) {5} D) {1, 3, 5, 7, 9}

16)                 

 

 

Answer the question True or False.

17) A statistical experiment can be almost any act of observation as long as the outcome is uncertain.

  1. A) True B) False

17)                 

 

 

18) The probability of a sample point is usually taken to be the relative frequency of the occurrence of the sample point in a very long series of repetitions of the experiment.

  1. A) True B) False

18)                 

 

 

19) In some experiments, we assign subjective probabilities, which can be interpreted as our degree of belief in the outcome.

  1. A) True B) False

19)                 

 

 

20) In any experiment with exactly four sample points in the sample space, the probability of each sample point is .25.

  1. A) True B) False

20)                 

 

 

21) An event may contain sample points that are not in the original sample space of the experiment.

For example, the experiment of rolling two dice has the following sample space:

 

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5,  1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

 

However, the event of rolling a sum of at least 11 on the two dice is {11, 12}.

  1. A) True B) False

21)                 

 

 

22) The probability of an event can be calculated by finding the sum of the probabilities of the individual sample points in the event and dividing by the number of sample points in the event.

  1. A) True B) False

22)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

Solve the problem.

23) A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment.

23)                                 

 

 

24) An experiment consists of randomly choosing a number between 1 and 10. Let A be the event that the number chosen is less than or equal to 7. List the sample points in A.

24)                                 

25) An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of randomly selecting one of the highlighters. Find the probability that a blue highlighter is chosen.

25)                                 

 

 

26) Suppose that an experiment has eight equally likely outcomes. What probability is assigned to each of the sample points?

26)                                 

 

 

27) The accompanying Venn diagram describes the sample space of a particular experiment and events A and B.  Suppose the sample points are equally likely.  Find P(A) and P(B).

 

 

28) The accompanying Venn diagram describes the sample space of a particular experiment

27)                                 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

28)                                 

and events A and B.  Suppose P(1) = P(2) = P(3) = P(4) =  1

16

and P(5) = P(6) = P(7) = P(8) =

P(9) = P(10) = 1 .  Find P(A) and P(B).

8

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

29) Probabilities of different types of vehicle-to-vehicle accidents are shown below:

 

Accident           Probability

Car to Car                0.59

Car to Truck            0.14

Truck to Truck       0.27

 

Find the probability that an accident involves a car.

  1. A) 27 B) 0.59 C) 0.73                                     D) 0.14

29)                 

30) A hospital reports that two patients have been admitted who have contracted Crohn’s disease.

Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where

S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.).

30)                 

 

Simple Events Probabilities
SS 0.52
SD 0.19
DS 0.16
DD 0.13

 

Find the probability that both patients survive.

  1. A) 13 B) 0.2704 C) 0.52                                     D) 0.35

 

 

31) A hospital reports that two patients have been admitted who have contracted Crohn’s disease.

Suppose our experiment consists of observing whether each patient survives or dies as a result of

the disease. The simple events and probabilities of their occurrences are shown in the table (where

S in the first position means that patient 1 survives, D in the first position means that patient 1 dies,

etc.).

31)                 

 

Simple Events Probabilities
SS 0.56
SD 0.20
DS 0.19
DD 0.05

 

Find the probability that at least one of the patients does not survive.

  1. A) 39 B) 0.20 C) 0.05                                     D) 0.44

 

 

32) A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:

32)                 

 

Color Number
Red 25
Brown 20
Green 20
Blue 15
Yellow 10
Orange 10

 

Find the probability that a randomly selected piece is either yellow or orange in color.

  1. A) 20 B) 20 C) 0.10                                     D) 10

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

33) A hospital reports that two patients have been admitted who have contracted Crohn’s disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.).

33)                                 

 

Simple Events Probabilities
SS 0.58
SD 0.12
DS 0.10
DD 0.20

 

Find the probability that neither patient survives.

 

 

34) In a sample of 750 of its online customers, a department store found that 420 were men.

Use this information to estimate the probability that a randomly selected online customer

is a man.

34)                                 

 

 

35) At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student receives some form of government -sponsored financial aid.

35)                                 

 

 

36) The manager of a warehouse club estimates that 7 out of 10 customers will donate a dollar to help a children’s hospital during an annual drive to benefit the hospital. Using the manager’s estimate, what is the probability that a randomly selected customer will donate a dollar?

36)                                 

 

 

37) A college has 85 male and 75 female fulltime faculty members. Suppose one fulltime faculty member is selected at random and the faculty member’s gender is observed.

 

  1. List the sample points for this experiment. b. Assign probabilities to the sample points.

37)                                 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

38) At a community college with 500 students, 120 students are age 30 or older. Find the probability that a randomly selected student is age 30 or older.

  1. A) .24 B) .30 C) .76                                       D) .12

38)                 

 

 

39) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical store?

  1. A) .78 B) .28 C) .22                                       D) .50

39)                 

40) A music store has 8 male and 12 female employees. Suppose one employee is selected at random and the employee’s gender is observed. List the sample points for this experiment, and assign probabilities to the sample points.

  1. A) {male, female}; P(male) = .4 and P(female) = .6
  2. B) {8, 12}; P(8) = .8 and P(12) = .12
  3. C) {8, 12}; P(8) = .5 and P(12) = .6
  4. D) {male, female}; P(male) = .8 and P(female) = .12

40)                 

 

 

41) An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. Assuming that each of the numbers between 1 and 10 is equally likely to be chosen, find P(E).

  1. A) .2 B) .5 C) .1                                         D) .8

41)                 

 

 

42) The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Find the probability that the number rolled on a single roll of this die is less than 4.

42)                 

 

Outcome 1 2 3 4 5 6
Probability .1 .1 .1 .2 .2 .3

 

  1. A) .5 B) .7 C) .3                                         D) .2

 

 

43) The table displays the probabilities for each of the outcomes when three fair coins are tossed and the number of heads is counted. Find the probability that the number of heads on a single toss of the three coins is at most 2.

43)                 

 

Outcome 0 1 2 3
Probability .125 .375 .375 .125

 

  1. A) .125 B) .500 C) .875                                     D) .750

 

 

44) At a certain university, one out of every 20 students is enrolled in a statistics course. If one student at the university is chosen at random, what is the probability that the student is enrolled in a statistics course?

44)                 

  1. A) 1

2

  1. B) 1

21

  1. C) 1

20

  1. D) 1

19

 

 

45) Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips.

45)                 

  1. A) 6

7

  1. B) 9

49

  1. C) 1

7

  1. D) 1

12

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

46) Three fair coins are tossed and either heads (H) or tails (T) is observed for each coin.

 

  1. List the sample points for this experiment. b. Assign probabilities to the sample points.
  2. Find the probability of the event A = {Three heads are observed}.
  3. Find the probability of the event B = {Exactly two heads are observed}.
  4. Find the probability of the event C = {At least two heads are observed}.

46)                                 

47) Two chips are drawn at random and without replacement from a bag containing three blue chips and one red chip.

 

  1. List the sample points for this experiment. b. Assign probabilities to the sample points.
  2. Find the probability of the event A = {Two blue chips are drawn}.
  3. Find the probability of the event B = {A blue chip and a red chip are drawn}. e.         Find the probability of the event C = {Two red chips are drawn}.

47)                                 

 

 

48) In an exit poll, 45% of voters said that the main issue affecting their choices of candidates was the economy, 35% said national security, and the remaining 20% were not sure. Suppose we select one of the voters who participated in the exit poll at random and ask for the main issue affecting his or her choices of candidates.

 

  1. List the sample points for this experiment.
  2. Assign reasonable probabilities to the sample points.
  3. Find the probability that the main issue affecting his or her choices was either the

economy or national security.

48)                                 

 

 

49) The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted.

49)                                 

 

gold gold silver gold bronze silver silver
bronze gold silver silver bronze silver gold
gold silver silver bronze bronze gold silver
gold gold bronze bronze

 

  1. List the sample points for this experiment. b. Find the probability of each sample point.
  2. What is the probability that the medal was not bronze?

 

 

50) The table shows the number of each type of book found at an online auction site during a recent search. Suppose that Juanita randomly chose one book to bid on and then noted its type.

50)                                 

 

Type of Book Number
Children’s 51,033
Fiction 141,114
Nonfiction 253,074
Educational 67,252

 

  1. List the sample points for this experiment. b. Find the probability of each sample point.
  2. What is the probability that the book was nonfiction or educational?

51) The table shows the number of each car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.

51)                                 

 

Type of Car Number
Sedan 7,204
Convertible 9,089
Wagon 20,418
SUV 13,691
Van 15,837
Hatchback 15,350
Total 81,589

 

  1. List the sample points for this experiment. b. Find the probability of each sample point.
  2. What is the probability that the car was a Van or an SUV?

 

 

52) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Suppose that one of the countries represented is chosen at random and the total numbers of medals won by that country is noted.

 

1           2          3           3           4           9           9          11        11

11         14        14        19        22         23        24        25        29 a.               List the sample points for this experiment.

  1. Find the probability of each sample point.
  2. What is the probability that the country won at least 20 total medals?

52)                                 

 

 

53) The following data represent the scores of 50 students on a statistics exam. Suppose that one of the 50 students is chosen at random and that student’s score is noted.

53)                                 

 

39 51 59 63 66 68 68 69 70 71
71 71 73 74 76 76 76 77 78 79
79 79 79 80 80 82 83 83 83 85
85 86 86 88 88 88 88 89 89 89
90 90 91 91 92 95 96 97 97 98

 

  1. What is the probability that the student’s score is 88?
  2. What is the probability that the student’s score is less than 60?
  3. What is the probability that the student’s score is between 70 and 79, inclusive?

 

 

54) Three companies (A, B, and C) are to be ranked first, second, and third in a list of companies with the highest customer satisfaction.

 

  1. List all the possible sets of rankings for these top three companies.
  2. Assuming that all sets of rankings are equally likely, what is the probability that

Company A will be ranked first, Company B second, and Company C third?

  1. Assuming that all sets of rankings are equally likely, what is the probability that

Company B will be ranked first?

54)                                 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Compute.

55)   7

4

 

 

 

  1. A) 840 B) 2 C) 35                                        D) 6

 

55)                 

 

 

56)   10

4

  1. A) 34 B) 210 C) 6                                          D) 5040

56)                 

 

 

57)   4

4

 

 

  1. A) 3 B) 4 C) 1                                           D) 6

57)                 

 

 

58)   4

0

 

 

  1. A) 4 B) 6 C) 3                                           D) 1

58)                 

 

 

59)   4

3

 

 

  1. A) 24 B) 1 C) 4                                           D) 3

59)                 

 

 

Compute the number of ways you can select n elements from N elements.

60) n = 3, N = 9

  1. A) 504 B) 3 C) 720                                      D) 84

60)                 

 

 

61) n = 2, N = 10

  1. A) 45 B) 8 C) 19                                        D) 90

61)                 

 

 

Solve the problem.

62) Which quantity is represented on the screen below?

 

  1. A) The number of sample points when a die is rolled and a coin is flipped
  2. B) The number of ways two dice can be rolled
  3. C) The number of ways two coins can be chosen from six coins
  4. D) The number of sample points when a coin is flipped six times

62)                 

 

 

63) Which expression is equal to   N  ?

n

63)                 

  1. A) N!

n!

  1. B) N!

N!(N n)!

  1. C) N!

(N n)!

  1. D) N!

n!(N n)!

64) Evaluate   8   .

2

64)                 

  1. A) 16 B) 56 C) 4                                          D) 28

 

 

65) Evaluate   6   .

0

65)                 

  1. A) 1 B) undefined C) 0                                          D) 6

 

 

66) Evaluate   7   .

7

66)                 

  1. A) 1 B) 7 C) 49                                        D) 14

 

 

67) Compute the number of ways you can select 3 elements from 7 elements.

  1. A) 343 B) 21 C) 10                                        D) 35

67)                 

 

 

68) There are 10 movies that Greg would like to rent but the store only allows him to have 4 movies at one time. In how many ways can Greg choose 4 of the 10 movies?

  1. A) 10,000 B) 40 C) 210                                      D) 5040

68)                 

 

 

69) Kim submitted a list of 12 movies to an online movie rental company. The company will choose 3 of the movies and ship them to her. If all movies are equally likely to be chosen, what is the probability that Kim will receive the three movies that she most wants to watch? Express the probability as a fraction.

69)                 

  1. A) 1

1728

  1. B) 1

1320

  1. C) 1

220

  1. D) 1

4

 

 

Answer the question True or False.

70) The quantity 0! is defined to be equal to 0.

  1. A) True B) False

70)                 

 

 

71) The combinations rule applies to situations in which the experiment calls for selecting n elements from a total of N elements, without replacing each element before the next is selected.

  1. A) True B) False

71)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

Solve the problem.

72) Compute   10  .                                                                                                                                                       72)                                 

6

 

 

73) Compute   5  .                                                                                                                                                         73)                                 

1

 

 

74) Compute the number of ways you can select n elements from N elements for n = 6 and N =

15.

74)                                 

 

 

75) In how many ways can a manager choose 3 of his 8 employees to work overtime helping with inventory?

75)                                 

76) The manager of an advertising department has asked her creative team to propose six new ideas for an advertising campaign for a major client. She will choose three of the six proposals to present to the client. (We will refer to the six proposals as A, B, C, D, E, and

F.)

 

  1. In how many ways can the manager select the three of the six proposals? List the possibilities.
  2. It is unlikely that the manager will randomly select three of the six proposals, but if she does what is the probability that she selects proposals A, D, and E?

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

Solve the problem.

1) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.

 

A: {The number is even}

B: {The number is less than 7}

 

Identify the sample points in the event A ∪ B.

  1. A) {1, 2, 3, 4, 5, 6, 7, 8, 10} B) {1, 2, 3, 4, 5, 6, 8, 10}
  2. C) {1, 2, 3, 4, 5, 6, 7, 9} D) {2, 4, 6}

 

 

1)

 

 

 

 

2) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.

 

A: {The number is even}

B: {The number is less than 7}

 

Identify the sample points in the event A ∩ B.

  1. A) {1, 2, 3, 4, 5, 6, 8, 10} B) {1, 2, 3, 4, 5, 6, 7, 8, 10}
  2. C) {2, 4, 6} D) {1, 2, 3, 4, 5, 6, 7, 9}

 

2)

 

 

 

 

3) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The sum of the numbers on the dice is 3}

B: {At least one of the dice shows a 2}

 

Identify the sample points in the event A ∪ B.

  1. A) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
  2. B) {(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} C) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)}
  3. D) {(1, 2), (2, 1)}

 

3)

 

 

 

 

4) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The sum of the numbers on the dice is 3}

B: {At least one of the dice shows a 2}

 

Identify the sample points in the event A ∩ B.

  1. A) {(1, 2), (2, 1)}
  2. B) {(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
  3. C) {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)}
  4. D) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}

 

4)

 

5) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The sum of the numbers on the dice is 4}

B: {The sum of the numbers on the dice is 11}

 

Identify the sample points in the event A ∪ B.

  1. A) {(1, 4), (2, 2), (4, 1), (5, 6), (6, 5)}
  2. B) {(1, 3), (2, 2), (3, 1), (5, 6), (6, 5)}
  3. C) {(1, 4), (2, 3), (3, 2), (4, 1), (5, 6), (6, 5)}
  4. D) There are no sample points in the event A ∪

 

5)

 

 

 

 

6) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.

 

A: {The number is even}

B: {The number is less than 7}

 

Which expression represents the event that the number is even or less than 7 or both?

  1. A) Ac B) A ∩ B C) Bc      D) A ∪ B

 

6)

 

 

 

 

7) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.

 

A: {The number is even}

B: {The number is less than 7}

 

Which expression represents the event that the number is both even and less than 7?

  1. A) Ac B) A ∪ B C) A ∩ B               D) Bc

 

7)

 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

8) A company evaluates its potential new employees using three criteria.

 

A: The applicant has a minimum college GPA of 3.0.

B: The applicant has relevant work experience.

C: The applicant has a sufficient score on an aptitude test.

 

  1. Write the event that an applicant meets all three criteria as a union or intersection of A,

B, and C.

  1. Write the event that an applicant meets at least one of the three criteria as a union or

intersection of A, B, and C.

 

8)

 

 

 

 

9) A consumer advocacy group rates the quality of a cellular service provider using three criteria.

 

A: Service is available at least 99% of the time.

B: Reception is clear at least 95% of the time.

C: Fewer than 5% of its customers have complaints about the quality of service.

 

  1. Describe the event represented by A ∩ B ∩ C. b. Describe the event represented by A ∪ B ∪ C.

 

9)

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

10) Fill in the blank. The                 of two events A and B is the event that either A or B or both occur.

  1. A) Venn diagram B) union C) complement                 D) intersection

 

10)

 

 

 

 

11) Fill in the blank. The                 of two events A and B is the event that both A and B occur.

  1. A) intersection B) union C) Venn diagram D) complement

 

11)

 

 

 

 

Answer the question True or False.

12) Unions and intersections of events are examples of compound events.

  1. A) True B) False

 

 

12)

 

 

 

 

13) Unions and intersections cannot be defined for more than two sets, so that A ∪ B ∪ C and A ∩ B ∩ C

are meaningless.

  1. A) True B) False

 

13)

 

 

 

 

14) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The sum of the numbers on the dice is 3}

B: {At least one of the dice shows a 2}

 

True or False: A ∪ B = B.

  1. A) True B) False

 

14)

 

 

 

 

15) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.

 

A: {Both chips are red}

B: {At least one of the chips is blue}

 

True or False: A ∩ B = B.

  1. A) True B) False

 

15)

 

Solve the problem.

16) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor

of a company’s success is customer service. A study was conducted to determine the customer

satisfaction levels for one overnight shipping business. In addition to the customer’s satisfaction level, the customers were asked how often they used overnight shipping. The results are shown in the following table:

 

 

16)

 

 

 

Frequency of Use            Satisfaction level

High       Medium               Low

TOTAL

< 2 per month

2 – 5 per month

> 5 per month   250         140         10

140         55           5

70           25           5              400

200

100

TOTAL   460         220         20           700

 

Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer had a high level of satisfaction and used the company more than five times per month?

 

  1. A) 7

10

 

  1. B) 4

5

 

  1. C) 3

10

 

  1. D) 1

10

 

 

 

 

17) Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The manager’s educational background was also noted. The data appear below:

 

Educational Background

 

17)

 

 

Manager

Rating

  1. S. Degree Some College College Degree  Master’s or Ph.D.

Total

Good

Fair

Poor      9              4              22           4

3              18           47           19

8              1              6              19           39

87

34

Total      20           23           75           42           160

 

What is the probability that a randomly chosen manager has earned at least one college degree?

 

  1. A) 15

32

 

  1. B) 117

160

 

  1. C) 21

80

 

  1. D) 43

160

 

 

 

 

18) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager’s educational background was also noted. The data appear below:

 

Educational Background

 

18)

 

 

Manager

Rating

  1. S. Degree Some College College Degree  Master’s or Ph.D.

Totals

Good

Fair

Poor      1              5              22           11

6              13           41           27

4              7              2              21           39

87

34

Totals    11           25           65           59           160

 

If we randomly selected one manager from this company, find the probability that he or she has an advanced (Master’s or Ph.D.) degree and is a good manager.

 

  1. A) 63

80

 

  1. B) 11

160

 

  1. C) 149

160

 

  1. D) 49

80

 

19) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below:

 

Number of Vehicles Involved

 

19)

 

 

Did Alcohol Play a Role?                1              2              3 or more            Totals

Yes

No          59           99           12

22           177         31           170

230

Totals    81           276         43           400

 

Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved more than a single vehicle?

 

  1. A) 3

100

 

  1. B) 81

400

 

  1. C) 319

400

 

  1. D) 43

400

 

 

 

 

20) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich.

Region

 

20)

 

 

NE          SE           SW         NW

<10,000                2%          6%          3%          0%

Population of City   10,000 – 100,000         15%        9%          12%        5%

>100,000              20%        4%          7%          17%

 

What is the probability that the restaurant is located in the northern portion of the United States?

  1. A) 0.37 B) 0.41 C) 0.59 D) 0.22

 

 

 

21) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich.

Region

 

21)

 

 

NE          SE           SW         NW

<10,000                9%          6%          3%          0%

Population of City   10,000 – 100,000         15%        2%          12%        5%

>100,000              20%        4%          8%          16%

 

What is the probability that the restaurant is located in a city with a population over 100,000 and in the southern portion of the United States?

  1. A) 0.12 B) 0.08 C) 0.04 D) 0.35

 

 

 

22) The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker’s political affiliation and type of job are noted.

 

22)

 

Political Affiliation

 

Republican          Democrat            Independent

 

Type of job         White collar

 

Blue Collar           18%

 

20%        9%

 

15%        6%

 

32%

 

Find the probability that the worker is a white collar worker affiliated with the Democratic Party.

  1. A) 0.48 B) 0.33 C) 0.09 D) 0.24

 

23) The table displays the probabilities for each of the six outcomes when rolling a particular unfair

die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and

let B be the event that the number rolled is odd. Find P(A ∪ B).

 

23)

 

 

Outcome             1              2              3              4              5              6

Probability          .1            .1            .1            .2            .2            .3

 

  1. A) .2 B) .7 C) .3       D) .5

 

 

 

24) The table displays the probabilities for each of the six outcomes when rolling a particular unfair

die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and

let B be the event that the number rolled is odd. Find P(A ∩ B).

 

24)

 

 

Outcome             1              2              3              4              5              6

Probability          .1            .1            .1            .2            .2            .3

 

  1. A) .2 B) .7 C) .3       D) .5

 

 

 

25) A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior).  The results are shown in the table below.

 

Find the probability that a randomly selected student is both a sophomore and drives a foreign automobile.

  1. A) 45/350 B) 65/205 C) 65/350             D) 65/110

 

25)

 

 

 

 

26) A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior).  The results are shown in the table below.

 

What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile?

  1. A) 215/350 B) 15/350 C) 230/350           D) 15/205

 

26)

 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

 

27) Suppose that an experiment has five sample points, E1, E2, E3, E4, E5, and that P(E1) = .2,

P(E2) = .3, P(E3) = .1, P(E4) = .1, and P(E5) = .3. If the events A and B are defined as

A = {E1, E2, E3} and B = {E2, E3, E4} find P(A ∩ B).

 

27)

 

28) Suppose that an experiment has five sample points, E1, E2, E3, E4, E5, and that P(E1) = .4,

P(E2) = .1, P(E3) = .1, P(E4) = .2, and P(E5) = .2. If the events A and B are defined as

A = {E1, E2, E5} and B = {E2, E3, E5} find P(A ∪ B).

 

28)

 

 

 

 

29) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a chicken sandwich.

Region

 

29)

 

 

NE          SE           SW         NW

<10,000                2%          6%          3%          0%

Population of City   10,000 – 100,000         15%        5%          12%        5%

>100,000              20%        4%          10%        18%

 

What is the probability that the restaurant is located in the western portion of the United

States?

 

 

 

30) The table shows the political affiliations and types of jobs for workers in a particular state.

Suppose a worker is selected at random within the state and the worker’s political

affiliation and type of job are noted.

 

30)

 

Political Affiliation

 

Republican          Democrat            Independent

 

Type of job         White collar

 

Blue Collar           17%

 

9%          19%

 

6%          15%

 

34%

 

What is the probability that the worker is a white collar Republican?

 

 

 

31) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The sum of the numbers on the dice is 6}

B: {At least one of the numbers 3}

 

  1. Identify the sample points in the event A ∪ B. b. Identify the sample points in the event A ∩ B. c.    Find P(A ∪ B).
  2. Find P(A ∩ B).

 

31)

 

 

 

 

32) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.

 

A: {Both chips are red}

B: {At least one of the chips is blue}

 

  1. Identify the sample points in the event A ∪ B. b. Find P(A ∪ B).

 

32)

 

33) The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.

 

33)

 

 

Type of Car         Number

Sedan   7,204

Convertible        9,089

Wagon  20,418

SUV       13,691

Van        15,837

Hatchback           15,350

Total      81,589

 

Events A and B are defined as follows.

 

A: {Convertible, SUV, Van}

B: {Fewer than 10,000 of the type of car were sold in June}

 

  1. Identify the sample points in the event A ∪ B. b. Identify the sample points in the event A ∩ B. c.    Find P(A ∪ B).
  2. Find P(A ∩ B).

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

 

34) In the game of Parcheesi each player rolls a pair of dice on each turn. In order to begin the game, you must roll a five on at least one die, or a total of five on both dice. Find the probability that a player begins the game on the first roll.

 

34)

 

  1. A) 5

18

 

  1. B) 1

6

 

  1. C) 11

36

 

  1. D) 15

36

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) Fill in the blank. The                      of an event A is the event that A does not occur.

  1. A) Venn diagram B) complement C) union                                 D) intersection

1)                    

 

 

2) The following Venn diagram shows the six possible outcomes when rolling a fair die. Let A be the event of rolling an even number and let B be the event of rolling a number greater than 1.

 

 

Which of the following expressions describes the event of rolling a 1?

  1. A) Bc B) B C) Ac                                        D) A ∪ B

2)                    

 

 

3) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events:

 

A: {The home is constructed of brick}

B: {The home is more than 30 years old}

 

In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30 years old.

  1. A) A B B) (A B)c C) A B                                  D) A Bc

3)                    

4) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events:

 

A: {The home is constructed of brick}

B: {The home is more than 30 years old}

D: {The home is heated with oil}

 

Which of the following describes the event B Dc?

  1. A) homes that are not older than 30 years old and heated with oil
  2. B) homes more than 30 years old that are not heated with oil
  3. C) homes more than 30 years old or homes that are not heated with oil
  4. D) homes more than 30 years old that are heated with oil

4)                    

 

 

5) An insurance company looks at many factors when determining how much insurance will cost for a home. Two of the factors are listed below:

 

A: {The home’s roof is less than 10 years old} B: {The home has a security system}

 

In the words of the problem, define the event Bc.

  1. A) The home is not less than 10 years old
  2. B) The home is less than 10 years old
  3. C) The home does not have a security system
  4. D) The home has a security system

5)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

6) A fair die is rolled one time. Let A be the event that an odd number is rolled. Describe the event Ac.

6)                                    

 

 

7) A fair die is rolled one time. Let B be the event {1, 2, 5}. List the sample points in the event

Bc.

7)                                    

 

 

8) A company evaluates its potential new employees using three criteria.

 

A: The applicant has a minimum college GPA of 3.0.

B: The applicant has relevant work experience.

D: The applicant has a sufficient score on an aptitude test.

 

Describe an applicant represented by A Bc D.

8)                                    

 

 

9) A consumer advocacy group rates the quality of a cellular service provider using three criteria.

 

A: Service is available at least 99% of the time.

B: Reception is clear at least 95% of the time.

D: Fewer than 5% of its customers have complaints about the quality of service.

 

Describe a cellular service provider represented by Ac Bc Dc.

9)                                    

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

10) If an event A includes the entire sample space, then P(Ac) = 0.

  1. A) True B) False

10)                 

 

 

11) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.

 

A: {Both chips are red}

B: {At least one of the chips is blue}

 

True or False: A = Bc.

  1. A) True B) False

11)                 

 

 

Solve the problem.

12) At a community college with 500 students, 120 students are age 30 or older. Find the probability

that a randomly selected student is less than 30 years old.

  1. A) .24 B) .76 C) .12                                       D) .30

12)                 

 

 

13) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is that probability that a a randomly selected online customer lives within 50 miles of a physical store?

  1. A) .28 B) .22 C) .50                                       D) .78

13)                 

 

 

14) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company’s success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer’s satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table:

14)                 

 

 

Frequency of Use

Satisfaction level

High             Medium             Low

 

TOTAL

< 2 per month

2 – 5 per month

> 5 per month

250                    140                    10

140                     55                       5

70                       25                      5

400

200

100

TOTAL 460                   220                    20 700

 

Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer did not have a high level of satisfaction with the company?

  1. A) 4

7

  1. B) 23

35

  1. C) 3

7

  1. D) 12

35

15) The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker’s political affiliation and type of job are noted.

15)                 

Political Affiliation

 

Republican Democrat Independent
 

Type of job

White collar

 

Blue Collar

19%

 

12%

14%

 

9%

15%

 

31%

 

Find the probability the worker is not an Independent.

  1. A) 33 B) 0.21 C) 0.46                                     D) 0.54

 

 

16) A local country club has a membership of 600 and operates facilities that include an 18 -hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 61% regularly use the golf course, 48% regularly use the tennis courts, and 4% use neither of these facilities regularly. What is the probability that a member regularly uses at least one of the golf or tennis facilities?

  1. A) .48 B) .13 C) .96                                       D) .4

16)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

17) Suppose that for a certain experiment P(A) = .37. Find P(Ac).                                                                17)                                 

 

 

18) Suppose that for a certain experiment the probability of a particular event occurring is .21.

Find the probability that this event does not occur.

18)                                 

 

 

19) Suppose that an experiment has five sample points, E1, E2, E3, E4, E5, and that P(E1) = .2, P(E2) = .3, P(E3) = .1, P(E4) = .1, and P(E5) = .3. If event A is defined as A = {E1, E2, E3}, find P(Ac).

19)                                 

 

 

20) In a sample of 750 of its online customers, a department store found that 420 were men.

Use this information to estimate the probability that a randomly selected online customer

is not a man.

20)                                 

 

 

21) At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student does not receive some form of government-sponsored financial aid.

21)                                 

 

 

22) The manager of a warehouse club estimates that 7 out of 10 customers will donate a dollar to help a children’s hospital during an annual drive to benefit the hospital. Using the manager’s estimate, what is the probability that a randomly selected customer will not donate a dollar?

22)                                 

23) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Event A is defined as follows.

 

A: {Both chips are red}

 

  1. Describe the event Ac.
  2. Identify the sample points in the event Ac. c. Find P(Ac).

23)                                 

 

 

24) The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.

24)                                 

 

Type of Car Number
Sedan 7,204
Convertible 9,089
Wagon 20,418
SUV 13,691
Van 15,837
Hatchback 15,350
Total 81,589

 

Event A is defined as follows.

 

A: {Convertible, SUV, Van}

 

  1. Identify the sample points in the event Ac. b. Find P(Ac).

 

 

25) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The two numbers rolled are different}

B: {At least one of the numbers is greater than 2}

 

  1. Identify the sample points in the event Ac. b. Identify the sample points in the event Bc.
  2. Identify the sample points in the event Ac Bc. d.    Identify the sample points in the event Ac Bc. e.    Find P(Ac Bc).
  3. Find P(Ac Bc).

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) A sample of 350 students was selected and each was asked the make of their automobile (foreign

or domestic) and their year in college (freshman, sophomore, junior, or senior).  The results are shown in the table below.

Which of the following events listed would be considered mutually exclusive events?

  1. A) The student is a senior and the student drives a domestic B) The student is a junior and the student is a freshman
  2. C) The student is a freshman and the student drives a foreign automobile
  3. D) The student is a junior and the student drives a domestic automobile

1)                    

 

 

2) If P(A B) = 1 and P(A B) = 0, then which statement is true?

  1. A) A and B are complementary B) A and B are both empty events.
  2. C) A and B are supplementary D) A and B are reciprocal events.

2)                    

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

3) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The two numbers rolled are different}

B: {At least one of the numbers is greater than 2}

 

Are the events A and B mutually exclusive? Explain.

3)                                    

 

 

4) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.

 

A: {Both chips are red}

B: {At least one of the chips is blue}

 

Are the events A and B mutually exclusive? Explain.

4)                                    

 

 

5) A number between 1 and 10, inclusive, is randomly chosen. Events A, B, C, and D are defined as follows.

 

A: {The number is even}

B: {The number is less than 7}

C: {The number is odd}

D: {The number is greater than 5}

 

Identify one pair of mutually exclusive events.

5)                                    

6) Three fair coins are tossed and either heads or tails is observed for each coin. Events A and

B are defined as follows.

 

A: {Three heads are observed}.

B: {Exactly two heads are observed}.

 

Is P(A B) equal to the sum of P(A) and P(B)? Explain.

6)                                    

 

 

7) The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.

7)                                    

 

Type of Car Number
Sedan 7,204
Convertible 9,089
Wagon 20,418
SUV 13,691
Van 15,837
Hatchback 15,350
Total 81,589

 

Events A and B are defined as follows.

 

A: {Convertible, SUV, Van}

B: {Fewer than 10,000 of the type of car were sold in June}

 

Is P(A B) equal to the sum of P(A) and P(B)? Explain.

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

8) If two events, A and B, are mutually exclusive, then P(A and B) = P(A) × P(B).

  1. A) True B) False

8)                    

 

 

9) An event and its complement are mutually exclusive.

  1. A) True B) False

9)                    

 

 

10) If A and B are mutually exclusive events, then P(A B) = 0.

  1. A) True B) False

10)                 

 

 

11) If events A and B are not mutually exclusive, then it is possible that P(A) + P(B) > 1.

  1. A) True B) False

11)                 

 

 

Solve the problem.

12) Suppose that for a certain experiment P(A) = .33 and P(B) = .29. If A and B are mutually exclusive events, find P(A B).

  1. A) .31 B) .62 C) .03                                       D) .38

12)                 

 

 

13) Suppose that for a certain experiment P(A) = .47 and P(B) = .25 and P(A B) = .14.  Find P(A B).

  1. A) .86 B) .58 C) .36                                       D) .72

13)                 

14) In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a woman or earning an A.

  1. A) .8 B) .25 C) .975                                     D) .625

14)                 

 

 

15) In a class of 30 students, 18 are men, 6 are earning a B, and no men are earning a B. If a student is randomly selected from the class, find the probability that the student is a man or earning a B.

  1. A) .8 B) .4 C) .24                                       D) .54

15)                 

 

 

16) In a box of 50 markers, 30 markers are either red or black and 20 are missing their caps. If 12 markers are either red or black and are missing their caps, find the probability that a randomly selected marker is red or black or is missing its cap.

  1. A) 1 B) .24 C) .76                                       D) .38

16)                 

 

 

17) In a box of 75 markers, 36 markers are either red or black and 15 are blue. Find the probability that a randomly selected marker is red or black or blue.

  1. A) .68 B) .24 C) .32                                       D) .51

17)                 

 

 

18) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager’s educational background was also noted. The data appear below:

 

Educational Background

18)                 

 

Manager

Rating

 

H. S. Degree Some College College Degree Master’s or Ph.D.

 

Totals

Good

Fair

Poor

2                         3                           21                             13

6                        19                          45                             17

4                         8                            7                              15

39

87

34

Totals 12                       30                          73                             45 160

 

What is the probability that a randomly chosen manager is either a good managers or has an advanced degree?

  1. A) 71

160

  1. B) 147

160

  1. C) 21

40

  1. D) 13

160

 

 

19) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below:

 

Number of Vehicles Involved

19)                 

 

Did Alcohol Play a Role? 1              2         3 or more Totals
Yes

No

54          100             16

29           171             30

170

230

Totals 83           271             46 400

 

Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved alcohol or a single car?

  1. A) 83

400

  1. B) 199

400

  1. C) 17

40

  1. D) 27

200

20) A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

What proportion of the employees are female or have been employed for more than 10 years?

  1. A) 110/130 B) 85/130 C) 25/130                               D) 25/65

20)                 

 

 

21) A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

What proportion of the employees are male or have been employed for less than 11 years?

  1. A) 42/65 B) 165/130 C) 120/130                             D) 45/130

21)                 

 

 

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

22) A local country club has a membership of 600 and operates facilities that include an

18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 60% regularly use the golf course,

44% regularly use the tennis courts, and 8% use both of these facilities regularly. Find the probability that a randomly selected member uses the golf or tennis facilities regularly.

22)                                 

 

 

23) Suppose that for a certain experiment P(A) = .37, P(B) = .69, and P(A B) = .23. Find P(A

B).

23)                                 

 

 

24) Suppose that for a certain experiment P(A) = 1 and P(B) = 1 , and events A and B are

24)                                 

3                         4

mutually exclusive. Find P(A B).

 

 

25) Suppose that for a certain experiment P(A) = .8 and P(B) = .9. Use the Additive Rule to explain why the events A and B can not be mutually exclusive.

25)                                 

 

 

26) Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a grouper is .19. Is enough information available to find the probability of catching a red snapper or a grouper? Explain. If possible, find the

probability of catching a red snapper or a grouper.

26)                                 

27) Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a fish that weighs less than 5 pounds is .45. Is enough information available to find the probability of catching a red snapper or a fish that

weighs less than 5 pounds? Explain. If possible, find the probability of catching a red snapper or a fish that weighs less than 5 pounds.

27)                                 

 

 

28) Suppose that 62% of the employees at a company are male and that 35% of the employees just received merit raises. If 20% of the employees are male and received a merit raise, what is the probability that a randomly chosen employee is male or received a merit raise?

28)                                 

 

 

29) Suppose that 80% of the employees of a company received cash or company stock as a bonus at the end of the year. If 60% of the employees received a cash bonus and 30% received stock, what is the probability that a randomly chosen employee received both cash and stock as a bonus?

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Solve the problem.

1) A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the probability that a green notepad is selected given that it is either blue or green.

1)                    

  1. A) 1

4

  1. B) 1

3

  1. C) 1

2

  1. D) 1

12

 

 

2) A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the probability that a yellow or pink notepad is selected given that it is either blue or green.

2)                    

  1. A) 1

4

  1. B) 1

2

  1. C) 1 D) 0

 

 

3) An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters.

An experiment consists of randomly selecting one of the highlighters and recording its color. Find the probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected.

3)                    

  1. A) 1

3

  1. B) 1 C) 1

2

  1. D) 0

 

 

4) In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a woman given that the student is earning an A.

4)                    

  1. A) 11

20

  1. B) 7

22

  1. C) 5

11

  1. D) 7

10

 

 

5) In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is earning an A given that the student is a woman.

5)                    

  1. A) 7

22

  1. B) 7

40

  1. C) 5

11

  1. D) 1

4

 

 

6) In a class of 30 students, 18 are men, 6 are earning a B, and no men are earning a B. If a student is randomly selected from the class, find the probability that the student is a man given that the student earning a B.

6)                    

  1. A) 1 B) 1

3

  1. C) 3

5

  1. D) 0

7) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company’s success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer’s satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table:

7)                    

 

 

Frequency of Use

Satisfaction level

High             Medium             Low

 

TOTAL

< 2 per month

2 – 5 per month

> 5 per month

250                    140                    10

140                     55                       5

70                       25                      5

400

200

100

TOTAL 460                   220                    20 700

 

A customer is chosen at random. Given that the customer uses the company two to five times per month, what is the probability that the customer expressed medium satisfaction with the company?

  1. A) 73

140

  1. B) 11

40

  1. C) 11

140

  1. D) 1

4

 

 

8) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager’s educational background was also noted. The data appear below:

 

Educational Background

8)                    

 

Manager

Rating

 

H. S. Degree Some College College Degree Master’s or Ph.D.

 

Totals

Good

Fair

Poor

5                         4                           23                              7

8                        15                          49                             15

9                         3                            2                              20

39

87

34

Totals 22                       22                          74                             42 160

 

Given that a manager is rated as fair, what is the probability that this manager has no college background?

  1. A) 1

20

  1. B) 8

87

  1. C) 4

11

  1. D) 101

160

 

 

9) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below:

 

Number of Vehicles Involved

9)                    

 

Did Alcohol Play a Role? 1             2        3 or more Totals
Yes

No

52           92             26

25         176            29

170

230

Totals 77         268            55 400

 

Given that an accident involved multiple vehicles, what is the probability that it involved alcohol?

  1. A) 26

55

  1. B) 13

200

  1. C) 118

323

  1. D) 59

200

10) A researcher investigated whether a student’s seat preference was related in any way to the gender of the student. The researcher divided a lecture room into three sections (1 -front, middle of the room, 2-front, sides of the classroom, and 3 -back of the classroom, both middle and sides) and noted where each student sat on a particular day of the class. The researcher’s summary table is provided below.

10)                 

 

Area 1      Area 2      Area 3 Total
Male

Female

16               8                 9

11               13              15

33

39

Total 27               21              24 72

 

Suppose a person sitting in the front, middle portion of the class is randomly selected to answer a question. Find the probability that the person selected is female.

  1. A) 11

27

  1. B) 9

13

  1. C) 11

72

  1. D) 11

39

 

 

11) The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of each car and its make (foreign or domestic):

 

Age of Car (in years)

11)                 

 

Make 0 – 2           3 – 5            6 – 10           over 10 Total
Foreign

Domestic

43               25                13                   19

41               27                12                   20

100

100

Total 84               52                25                   39 200

 

A car was randomly selected from the lot. Given that the car selected was a foreign car, what is the probability that it was older than 2 years old?

  1. A) 43

116

  1. B) 57

116

  1. C) 43

100

  1. D) 57

100

 

 

12) A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior).  The results are shown in the table below.

Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile.

  1. A) 10/35 B) 15/350 C) 25/35                                  D) 15/205

12)                 

13) A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

Suppose an employee has been randomly selected from this company. Given that the employee is male, find the probability that they have worked for the company for more than 10 years?

  1. A) 20/30 B) 75/130 C) 20/65                                  D) 20/130

13)                 

 

 

14) The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker’s political affiliation and type of job are noted.

14)                 

Political Affiliation

 

Republican Democrat Independent
 

Type of job

White collar

 

Blue Collar

10%

 

9%

19%

 

15%

12%

 

35%

 

Given that the worker is a Democrat, what is the probability that the worker has  a white collar job.

  1. A) 339 B) 0.559 C) 0.607                                  D) 0.463

 

 

15) A local country club has a membership of 600 and operates facilities that include an 18 -hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 57% regularly use the golf course, 48% regularly use the tennis courts, and 9% use both of these facilities regularly. Given that a randomly selected member uses the tennis courts regularly, find the probability that they also use the golf course regularly.

  1. A) .1875 B) .4737 C) .7164                                  D) .1343

15)                 

 

 

16) For two events, A and B, P(A) = .4, P(B) = .7, and P(A B) = .2. Find P(A | B).

  1. A) .08 B) .5 C) .14                                       D) .29

16)                 

 

 

17) For two events, A and B, P(A) = 1 , P(B) = 1 , and P(A B) = 1 . Find P(B | A).

17)                 

 

  1. A) 1

12

2                  3

  1. B) 3

4

4

  1. C) 1

2

  1. D) 1

8

 

 

18) For two events, A and B, P(A) = .6, P(B) = .8, and P(A | B) = .5. Find P(A B).

  1. A) .625 B) .3 C) .4                                         D) .833

18)                 

 

 

19) For two events, A and B, P(A) = 3 , P(B) = 2 , and P(B | A) = 5 . Find P(A B).

19)                 

 

  1. A) 5

8

4                  3

  1. B) 5

9

6

  1. C) 9

10

  1. D) 1

2

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.

 

20) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. It further estimates that 39 out of every 100 of its online customers is a man who does not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer is a man given that the customer does not live within 50 miles of a physical store?

20)                                 

 

 

21) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich.

Region

21)                                 

 

NE SE SW NW
<10,000 5% 6% 3% 0%
Population of City   10,000 – 100,000 15% 6% 12% 5%
>100,000 20% 4% 7% 17%

 

What is the probability that the restaurant is located in a city with a population over

100,000, given that it is located in the southwestern United States?

 

 

22) The table shows the political affiliations and types of job for workers in a particular state.

Suppose a worker is selected at random within the state and the worker’s political affiliation and type of job are noted.

22)                                 

Political Affiliation

 

Republican Democrat Independent
 

Type of job

White collar

 

Blue Collar

19%

 

14%

10%

 

20%

12%

 

25%

 

Given that a worker is a blue collar worker, what is the probability that the worker is a

Democrat?

 

 

23) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.

 

A: {The number is even}

B: {The number is less than 7}

 

Find P(A | B) and P(B | A).

23)                                 

 

 

24) A pair of fair dice is tossed. Events A and B are defined as follows.

 

A: {The sum of the dice is 7}

B: {At least one of the numbers is 3}

 

Find P(A | B) and P(B | A).

24)                                 

25) The table shows the number of each Ford car sold in the United States in June 2006.

Suppose the sales record for one of these cars is randomly selected and the type of car is identified.

25)                                 

 

Type of Car Number
Sedan 7,204
Convertible 9,089
Wagon 20,418
SUV 13,691
Van 15,837
Hatchback 15,350
Total 81,589

 

Events A and B are defined as follows.

 

A: {Convertible, SUV, Van}

B: {Fewer than 10,000 of the type of car were sold in June 2006}

 

Find P(A | B) and P(B | A).

 

 

26) Suppose that 62% of the employees at a company are male and that 35% of the employees just received merit raises. If 20% of the employees are male and received a merit raise, what is the probability that a randomly chosen employee is male given that the employee received a merit raise?

26)                                 

 

 

27) The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and let B be the event that the number rolled is odd.

27)                                 

 

Outcome 1 2 3 4 5 6
Probability .1 .1 .1 .2 .2 .3

 

Find P(A | B).

 

 

28) The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted.

28)                                 

 

gold gold silver gold bronze silver silver
bronze gold silver silver bronze silver gold
gold silver silver bronze bronze gold silver
gold gold bronze bronze

 

Given that the medal is not bronze, what is the probability that the medal is gold?

29) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics.

 

1          2           3           3           4           9           9           11       11

 

11        14         14        19        22        23        24         25       29

 

Suppose that one of the countries represented is selected at random and the total number of medals won by that country is noted. What is the probability that the country won at least 25 medals given that the country did not win fewer than 10 medals?

29)                                 

 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

 

Answer the question True or False.

30) The conditional probability of event A given that event B has occurred is written as P(B | A).

  1. A) True B) False

30)                 

 

 

31) If A and B are mutually exclusive events, then P(A | B) = 0.

  1. A) True B) False

31)                 

 

 

32) For all events A and B, the conditional probabilities P(A | B) and P(B | A) are equal.

  1. A) True B) False

32)                 

 

 

33) If every sample point in event B is also a sample point in event A, then P(A | B) = 1.

  1. A) True B) False

33)                 

 

 

34) For any events A and B, P(A | B) + P(Ac | B) = 1, meaning given that B occurs either A occurs or A

does not occur.

  1. A) True B) False

34)                 

 

 

35) For any events A and B, P(A | B) + P(A | Bc) = 1, meaning given that A occurs either B occurs or B

does not occur.

  1. A) True B) False