Exam

Name___________________________________

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

Express the indicated degree of likelihood as a probability value.

1) “You have a 50-50 chance of choosing the correct answer.”

A) 0.50 B) 50 C) 0.9 D) 0.25

1)

2) “There is a 40% chance of rain tomorrow.”

A) 0.40 B) 4 C) 0.60 D) 40

2)

3) “You cannot determine the exact decimal-number value of π.”

A) 0 B) 0.5 C) 3.14 D) 1

3)

4) “Your mother could not have died two years before you were born.”

A) 0.5 B) 0 C) 0.25 D) 1

4)

5) “It will definitely turn dark tonight.”

A) 0.30 B) 1 C) 0.5 D) 0.67

5)

6) “You have one chance in ten of winning the race.”

A) 0.10 B) 0.90 C) 1 D) 0.5

6)

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

Solve the problem.

7) (a) Simulate the experiment of sampling 100 four-child families to estimate the probability

that a four-child family has three girls. Assume that the outcomes “have a girl” and “have a boy”

are equally likely.

(b) Simulate the experiment of sampling 1000 four-child families to estimate the probability

that a four-child family has three girls. Assume that the outcomes “have a girl” and “have a boy”

are equally likely.

The classical probability that a four-child family has three girls is 1

4 .

Compare the results of (a) and (b) to the probability that would be obtained using the classical

method.

Which answer was closer to the probability that would be obtained using the classical method? Is

this what you would expect?

7)

1

8) (a) Use a graphing calculator or statistical software to simulate drawing a card from a standard

deck 100 times (with replacement of the card after each draw). Use an integer distribution with

numbers 1 through 4 and use the results of the simulation to estimate the probability of getting a

spade when a card is drawn from a standard deck.

(b) Simulate drawing a card from a standard deck 400 times (with replacement of the card after

each draw). Estimate the probability of getting a spade when a card is drawn from a standard

deck.

Compare the results of (a) and (b) to the probability that would be obtained using the classical

method.

Which simulation resulted in the closest estimate to the probability that would be obtained using

the classical method? Is this what you would expect?

8)

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

Find the indicated probability.

9) A sample space consists of 197 separate events that are equally likely. What is the probability of

each?

A) 197 B) 1

197 C) 0 D) 1

9)

10) On a multiple choice test, each question has 7 possible answers. If you make a random guess on the

first question, what is the probability that you are correct?

A) 1 B) 0 C) 1

7 D) 7

10)

11) A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

A) 11

12 B) 5

6 C) 1

12 D) 10

11)

12) A bag contains 2 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected

from the bag, what is the probability that it is blue?

A) 1

7 B) 1

4 C) 1

9 D) 1

3

12)

13) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice

will be 5?

A) 5

6 B) 8

9 C) 1

9 D) 4

13)

14) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap

years.

A) 1

31 B) 1

365 C) 1

12 D) 31

365

14)

15) A class consists of 50 women and 21 men. If a student is randomly selected, what is the probability

that the student is a woman?

A) 50

21 B) 50

71 C) 21

71 D) 1

71

15)

2

Provide an appropriate response.

16) A question has five multiple-choice answers. Find the probability of guessing an incorrect answer.

A) 3

5 B) 4

5 C) 5

2 D) 1

5

16)

17) A question has five multiple-choice questions. Find the probability of guessing the correct answer.

A) 4

5 B) 2

5 C) 5

4 D) 1

5

17)

18) A single die is rolled twice. The set of 36 equally likely outcomes is {(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)}. Find the

probability of getting two numbers whose sum is greater than 9.

A) 1

4 B) 1

12 C) 1

6 D) 6

18)

19) A single die is rolled twice. The set of 36 equally likely outcomes is {(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)}. Find the

probability of getting two numbers whose sum is less than 13.

A) 1

2 B) 0 C) 1

4 D) 1

19)

20) A single die is rolled twice. The set of 36 equally likely outcomes is {(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)}. Find the

probability of getting two numbers whose sum is greater than 9 and less than 13.

A) 0 B) 7

36 C) 5

36 D) 1

6

20)

Answer the question.

21) Which of the following cannot be a probability?

A) -1 B) 0 C) 1

2 D) 1

21)

22) Which of the following cannot be a probability?

A) 5

3 B) 1

2 C) 2

3 D) 3

5

22)

23) What is the probability of an event that is certain to occur?

A) 0.99 B) 1 C) 0.5 D) 0.95

23)

24) What is the probability of an impossible event?

A) 0 B) -1 C) 0.1 D) 1

24)

3

25) On a multiple choice test with four possible answers for each question, what is the probability of

answering a question correctly if you make a random guess?

A) 1 B) 3

4 C) 1

4 D) 1

2

25)

Provide an appropriate response.

26) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land

on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.

Find the probability that the arrow will land on 2 or 3.

A) 3

2 B) 1 C) 2 D) 2

5

26)

27) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land

on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.

Find the probability that the arrow will land on an odd number.

A) 2

5 B) 1 C) 3

5 D) 0

27)

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

28) Use the pie chart, which shows the number of Congressional Medal of Honor recipients in the

United States, to find the probability that a randomly chosen recipient served in the Navy.

28)

4

29) Use the pie chart, which shows the number of Congressional Medal of Honor recipients in the

United States, to find the probability that a randomly chosen recipient did not serve in the

Marines.

29)

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

Use the empirical rule to solve the problem.

30) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120

mmHg and a standard deviation of 12 mmHg. What is the probability than an 18-year-old women

will have a systolic blood pressure between 96 mmHg and 144 mmHg?

A) 0.997 B) 0.95 C) 0.68

30)

Solve the problem.

31) A probability experiment is conducted in which the sample space of the experiment is

S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {8, 9, 10, 11, 12}. Assume that each outcome is

equally likely. List the outcomes in Ac. Find P(Ac).

A) {5, 6, 7, 12, 13, 14, 15}; 7

11 B) {8, 9, 10, 11, 12}; 5

11

C) {13, 14, 15}; 3

11 D) {5, 6, 7, 13, 14, 15}; 6

11

31)

32) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 10.

Express the probability as a simplified fraction.

A) 12

13 B) 1

13 C) 1

10 D) 9

10

32)

33) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a spade.

Express the probability as a simplified fraction.

A) 4

13 B) 3

4 C) 1

4 D) 2

5

33)

5

34) In 5-card poker, played with a standard 52-card deck, 2,598,960 different hands are possible. If

there are 624 different ways a “four-of-a-kind” can be dealt, find the probability of not being dealt

a “four-of-a-kind”. Express the probability as a fraction, but do not simplify.

A) 625

2,598,960 B) 624

2,598,960 C) 2,598,336

2,598,960 D) 1248

2,598,960

34)

35) A certain disease only affects men 20 years of age or older. The chart shows the probability that a man

with the disease falls in the given age group. What is the probability that a randomly selected man with the

disease is not between the ages of 55 and 64?

Age Group Probability

20-24 0.004

25-34 0.006

35-44 0.14

45-54 0.29

55-64 0.32

65-74 0.17

75+ 0.07

A) 0.29 B) 0.24 C) 0.32 D) 0.68

35)

36) A certain disease only affects men 20 years of age or older. The chart shows the probability that a man

with the disease falls in the given age group. What is the probability that a randomly selected man with the

disease is between the ages of 35 and 64?

Age Group Probability

20-24 0.004

25-34 0.006

35-44 0.14

45-54 0.29

55-64 0.32

65-74 0.17

75+ 0.07

A) 0.75 B) 0.32 C) 0.14 D) 0.29

36)

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

of a company’s success has been proven time and again to be customer service. A study was

conducted to study 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. What is the probability that a

respondent did not have a medium level of satisfaction with the company? Round the the nearest

hundredth.

Frequency of Use High

Satisfaction level

Medium Low TOTAL

< 2 per month 250 140 10 400

2 – 5 per month 140 55 5 200

> 5 per month 70 25 5 100

TOTAL 460 220 20 700

A) 0.31 B) 0.29 C) 0.69 D) 0.71

37)

6

38) A sample of 255 shoppers at a large suburban mall were asked two questions: (1) Did you see a

television ad for the sale at department store X during the past 2 weeks? (2) Did you shop at

department store X during the past 2 weeks? The responses to the questions are summarized in the

table. What is the probability that a randomly selected shopper from the 255 questioned did not shop

at department store X? Round the the nearest thousandth.

Shopped at X Did Not Shop at X

Saw ad 135 25

Did not see ad 25 70

A) 0.627 B) 0.275 C) 0.373 D) 0.098

38)

39) After completing an inventory of three warehouses, a golf club shaft manufacturer described its

stock of 12,246 shafts with the percentages given in the table. Suppose a shaft is selected at random

from the 12,246 currently in stock, and the warehouse number and type of shaft are observed. Find

the probability that the shaft was produced in a warehouse other than warehouse 1. Round the the

nearest hundredth.

Type of Shaft

Regular Stiff Extra Stiff

1 19% 8% 17%

Warehouse 2 14% 7% 7%

3 10% 18% 0%

A) 0.44 B) 0.76 C) 0.43 D) 0.56

39)

40) The breakdown of workers in a particular state according to their political affiliation and type of job held is

shown here. Suppose a worker is selected at random within the state and the worker’s political affiliation

and type of job are noted. Find the probability the worker is not an Independent. Round the the nearest

hundredth.

Political Affiliation

Republican Democrat Independent

White collar 7% 16% 9%

Type of job

Blue Collar 14% 18% 36%

A) 0.23 B) 0.32 C) 0.45 D) 0.55

40)

41) A probability experiment is conducted in which the sample space of the experiment is

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {3, 4, 5, 6} and event B = {11, 12, 13}.

Assume that each outcome is equally likely. List the outcomes in A and B. Are A and B mutually

exclusive?

A) {3, 4, 5, 6, 11, 12, 13}; yes B) { }; no

C) {3, 4, 5, 6, 11, 12, 13}; no D) { }; yes

41)

42) The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.3, what is P(A or B)?

A) 0.06 B) 0 C) 0.5 D) 0.1

42)

43) The table lists the drinking habits of a group of college students. If a student is chosen at random, find the

probability of getting someone who is a regular or heavy drinker. Round your answer to three decimal

places.

Sex Non-drinker Regular Drinker Heavy Drinker Total

Man 135 44 5 184

Woman 187 21 6 214

Total 322 65 11 398

A) 0.191 B) 0.126 C) 0.218 D) 0.658

43)

7

44) The table lists the drinking habits of a group of college students. If a student is chosen at random, find the

probability of getting someone who is a man or a woman. Round your answer to three decimal places.

Sex Non-drinker Regular Drinker Heavy Drinker Total

Man 135 69 5 209

Woman 187 21 12 220

Total 322 90 17 429

A) 0.249 B) 1 C) 0.751 D) 0.923

44)

45) The table lists the drinking habits of a group of college students. If a student is chosen at random,

find the probability of getting someone who is a non-drinker. Round your answer to three decimal

places.

Sex Non-drinker Regular Drinker Heavy Drinker Total

Man 135 49 5 189

Woman 187 21 6 214

Total 322 70 11 403

A) 0.799 B) 1 C) 0.201 D) 0.933

45)

46) The distribution of Bachelor’s degrees conferred by a university is listed in the table. Assume that a student

majors in only one subject. What is the probability that a randomly selected student with a Bachelor’s

degree majored in Physics or Philosophy? Round your answer to three decimal places.

Major Frequency

Physics 226

Philosophy 208

Engineering 86

Business 176

Chemistry 222

A) 0.246 B) 0.473 C) 0.527 D) 0.227

46)

47) The distribution of Bachelor’s degrees conferred by a university is listed in the table. Assume that a student

majors in only one subject. What is the probability that a randomly selected student with a Bachelor’s

degree majored in Business, Chemistry or Engineering? Round your answer to three decimal places.

Major Frequency

Physics 216

Philosophy 207

Engineering 89

Business 170

Chemistry 215

A) 0.289 B) 0.528 C) 0.472 D) 0.339

47)

48) A probability experiment is conducted in which the sample space of the experiment is

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {8, 9, 10, 11} and event

B = {10, 11, 12, 13, 14}. Assume that each outcome is equally likely. List the outcomes in A or B.

Find P(A or B).

A) {8, 9, 10, 11, 12, 12, 13, 14}; 3

5 B) {10, 11}; 2

15

C) {8, 9, 10, 11, 12, 13, 14}; 7

15 D) {8, 9, 10, 11, 13, 14}; 2

5

48)

49) The events A and B are mutually exclusive. If P(A) = 0.1 and P(B) = 0.5, what is P(A and B)?

A) 0.05 B) 0.6 C) 0.5 D) 0

49)

8

50) Given that P(A or B) = 1

2 , P(A) = 1

7 , and P(A and B) = 1

8 , find P(B). Express the probability as a

simplified fraction.

A) 43

56 B) 27

56 C) 29

56 D) 17

112

50)

51) The table lists the drinking habits of a group of college students. If a student is chosen at random,

find the probability of getting someone who is a man or a non-drinker. Round your answer to three

decimal places.

Sex Non-drinker Regular Drinker Heavy Drinker Total

Man 135 52 5 192

Woman 187 21 9 217

Total 322 73 14 409

A) 0.927 B) 0.948 C) 0.822 D) 0.941

51)

52) The table lists the drinking habits of a group of college students. If a student is chosen at random, find the

probability of getting someone who is a woman or a heavy drinker. Round your answer to three decimal

places.

Sex Non-drinker Regular Drinker Heavy Drinker Total

Man 135 31 5 171

Woman 187 21 15 223

Total 322 52 20 394

A) 0.117 B) 0.909 C) 0.868 D) 0.579

52)

53) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is a

queen or a club. Express the probability as a simplified fraction.

A) 2

13 B) 4

13 C) 3

13 D) 7

52

53)

54) One hundred people were asked, “Do you favor stronger laws on gun control?” Of the 33 that

answered “yes” to the question, 14 were male. Of the 67 that answered “no” to the question, six were

male. If one person is selected at random, what is the probability that this person answered “yes” or

was a male? Round the the nearest hundredth.

A) 0.67 B) 0.39 C) 0.53 D) 0.13

54)

55) The below table shows the probabilities generated by rolling one die 50 times and noting the up face.

What is the probability of getting an odd up face and a two or less? Round the the nearest hundredth.

Roll 1 2 3 4 5 6

Probability 0.22 0.10 0.18 0.12 0.18 0.20

A) 0.90 B) 0.66 C) 0.32 D) 0.68

55)

56) You roll two dice and total the up faces. What is the probability of getting a total of 8 or two up

faces that are the same? Round the the nearest hundredth.

A) 0.50 B) 0.28 C) 0.31 D) 0.33

56)

9

57) Consider the data in the table shown which represents the marital status of males and females 18 years or

older in the United States in 2003. Determine the probability that a randomly selected U.S. resident 18

years or older is divorced or a male? Round to the nearest hundredth.

Males

(in millions)

Females

(in millions)

Total

(in millions)

Never married 28.6 23.3 51.9

Married 62.1 62.8 124.9

Widowed 2.7 11.3 14.0

Divorced 9.0 12.7 21.7

Total (in millions) 102.4 110.1 212.5

Source: U.S. Census Bureau, Current Population reports

A) 0.58 B) 0.54 C) 0.04 D) 0.50

57)

58) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a

ten, a king or a diamond. Round to the nearest hundredth.

A) 0.37 B) 0.31 C) 0.40 D) 0.29

58)

59) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a

jack, a three, a club or a diamond. Round to the nearest hundredth.

A) 0.50 B) 0.65 C) 0.58 D) 0.15

59)

60) Two dice are rolled. What is the probability of having both faces the same (doubles) or a total of 4

or 10? Round to the nearest hundredth.

A) 0.33 B) 0.28 C) 0.06 D) 0.15

60)

61) A probability experiment is conducted in which the sample space of the experiment is

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {5, 6, 7, 8} and event B = {7, 8, 9, 10, 11}.

Assume that each outcome is equally likely. List the outcomes in A and B. Are A and B mutually

exclusive? Find P(A and B)

A) {7, 8}; no; 2

15 B) {5, 6, 7, 8, 9, 10, 11}; no; 7

15

C) {7, 8}; yes; 2

15 D) {5, 6, 7, 8, 9, 10, 11}; yes; 7

15

61)

62) The complement of 4 heads in the toss of 4 coins is

A) All tails B) Three heads C) At least one tail D) Exactly one tail

62)

63) 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 69% regularly use the golf course, 47% regularly use the tennis

courts, and 3% use neither of these facilities regularly. What percentage of the 600 use at least one

of the golf or tennis facilities?

A) 97% B) 113% C) 19% D) 3%

63)

64) A game has three outcomes. The probability of a win is 0.4, the probability of tie is 0.5, and the

probability of a loss is 0.1. What is the probability of not winning in a single play of the game.

A) 0.6 B) 0.1 C) 0.33 D) 0.5

64)

10

65) In the game of craps two dice are rolled and the up faces are totaled. If the person rolling the dice

on the first roll rolls a 7 or an 11 total they win. If they roll a 2, 3, or 12 on the first roll they lose. If

they roll any other total then on subsequent rolls they must roll that total before rolling a 7 to win.

What is the probability of winning on the first roll?

A) 0.17 B) 0.50 C) 0.06 D) 0.22

65)

Find the indicated probability. Give your answer as a simplified fraction.

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

of a company’s success has been proven time and again to be customer service. A study was

conducted to study 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. A customer is chosen at random.

Given that the customer uses the company less than two times per month, what is the probability

that they expressed low satisfaction with the company?

Frequency of Use High

Satisfaction level

Medium Low TOTAL

< 2 per month 250 140 10 400

2 – 5 per month 140 55 5 200

> 5 per month 70 25 5 100

TOTAL 460 220 20 700

A) 41

70 B) 1

40 C) 1

70 D) 1

2

66)

67) The managers of a corporation were surveyed to determine the background that leads to a successful

manager. Each manager 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. Given that a manager is only a

fair manager, what is the probability that this manager has no college background?

Educational Background

Manager

Rating H. S. Degree Some College College Degree Master’s or Ph.D. Totals

Good 5 6 24 4 39

Fair 8 18 44 17 87

Poor 3 2 1 28 34

Totals 16 26 69 49 160

A) 19

32 B) 1

2 C) 1

20 D) 8

87

67)

68) The managers of a corporation were surveyed to determine the background that leads to a successful

manager. Each manager 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. Given that a manager is only a

fair manager, what is the probability that this manager has a college degree?

Educational Background

Manager

Rating H. S. Degree Some College College Degree Master’s or Ph.D. Totals

Good 4 2 28 5 39

Fair 8 14 41 24 87

Poor 7 5 3 19 34

Totals 19 21 72 48 160

A) 41

160 B) 24

29 C) 9

20 D) 41

87

68)

11

69) The managers of a corporation were surveyed to determine the background that leads to a successful

manager. Each manager 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. Given that a manager is a

good manager, what is the probability that this manager has some college background?

Educational Background

Manager

Rating H. S. Degree Some College College Degree Master’s or Ph.D. Totals

Good 5 1 28 5 39

Fair 7 15 46 19 87

Poor 4 8 9 13 34

Totals 16 24 83 37 160

A) 1

24 B) 28

39 C) 1

39 D) 1

160

69)

70) A study was recently done that emphasized the problem we all face with drinking and driving.

Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were

the number of vehicles involved and whether alcohol played a role in the accident. The numbers

are shown below. Given that an accident involved multiple vehicles, what is the probability that it

involved alcohol?

Number of Vehicles Involved

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

Yes 60 99 11 170

No 28 170 32 230

Totals 88 269 43 400

A) 55

156 B) 11

400 C) 11

40 D) 11

43

70)

71) A researcher at a large university wanted to investigate if a student’s seat preference was related in

any way to the gender of the student. The researcher divided the 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 his students sat on a particular day of the class. The researcher’s

summary table is provided below. Suppose a person sitting in the front, middle portion of the class is

randomly selected to answer a question. Find the probability the person selected is a female.

Area (1) Area (2) Area (3) Total

Males 20 6 7 33

Females 13 12 14 39

Total 33 18 21 72

A) 13

33 B) 13

72 C) 1

3 D) 11

13

71)

72) 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 his car and its make (foreign or domestic). 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? Age of Car (in years)

Make 0 – 2 3 – 5 6 – 10 over 10 Total

Foreign 35 30 14 21 100

Domestic 44 26 12 18 100

Total 79 56 26 39 200

A) 13

20 B) 35

121 C) 65

121 D) 7

20

72)

12

73) 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 his car and its make (foreign or domestic). A car was randomly

selected from the lot. Given that the car selected was a domestic car, what is the probability that it

was older than 2 years?

Age of Car (in years)

Make 0 – 2 3 – 5 6 – 10 over 10 Total

Foreign 40 23 10 27 100

Domestic 42 21 14 23 100

Total 82 44 24 50 200

A) 21

41 B) 41

100 C) 29

50 D) 21

100

73)

74) 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 his car and its make (foreign or domestic).

Age of Car (in years)

Make 0 – 2 3 – 5 6 – 10 over 10 Total

Foreign 38 30 10 22 100

Domestic 43 28 13 16 100

Total 81 58 23 38 200

A car was randomly selected from the lot. Given that the car selected is older than two years old, find the

probability that it is not a foreign car.

A) 31

50 B) 57

100 C) 62

119 D) 57

119

74)

Find the indicated probability. Give your answer as a decimal rounded to the nearest thousandth.

75) A fast-food restaurant chain with 700 outlets in the United States describes the geographic location

of its restaurants with the accompanying table of percentages. A restaurant is to be chosen at

random from the 700 to test market a new style of chicken. Given that the restaurant is located in

the eastern United States, what is the probability it is located in a city with a population of at least

10,000?

Region

NE SE SW NW

<10,000 5% 6% 3% 0%

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

>100,000 20% 4% 3% 25%

A) 0.212 B) 0.41 C) 0.788 D) 0.477

75)

76) After completing an inventory of three warehouses, a golf club shaft manufacturer described its stock of

12,246 shafts with the percentages given in the table. Suppose a shaft is selected at random from the 12,246

currently in stock, and the warehouse number and type of shaft are observed. Given that the shaft is

produced in warehouse 2, find the probability it has an extra stiff shaft.

Type of Shaft

Regular Stiff Extra Stiff

1 19% 8% 5%

Warehouse 2 14% 2% 33%

3 1% 18% 0%

A) 0.868 B) 0.54 C) 0.673 D) 0.611

76)

13

77) The breakdown of workers in a particular state according to their political affiliation and type of job held is

shown here. Suppose a worker is selected at random within the state and the worker’s political affiliation

and type of job are noted. Given the worker is a Democrat, what is the probability that the worker is in a

white collar job.

Political Affiliation

Republican Democrat Independent

White collar 19% 12% 18%

Type of job

Blue Collar 8% 13% 30%

A) 0.403 B) 0.48 C) 0.245 D) 0.194

77)

78) 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 65% regularly use the golf course, 41% regularly use the tennis

courts, and 8% use neither 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.

A) 0.132 B) 0.341 C) 0.215 D) 0.152

78)

Provide an appropriate response.

79) There are 30 chocolates in a box, all identically shaped. There are 11 filled with nuts, 10 filled with

caramel, and 9 are solid chocolate. You randomly select one piece, eat it, and then select a second

piece. Are the given events independent or dependent?

A) dependent B) independent

79)

80) Numbered disks are placed in a box and one disk is selected at random. There are 6 red disks

numbered 1 through 6, and 7 yellow disks numbered 7 through 13. In an experiment a disk is

selected, the number and color noted, replaced, and then a second disk is selected. Are the given

events independent or dependent?

A) dependent B) independent

80)

81) After completing an inventory of three warehouses, a golf club shaft manufacturer described its

stock of 12, 246 shafts with percentages given in the table. Is the event of selecting a shaft

independent of the warehouse? Answer Yes or No.

A) No B) Yes

81)

Solve the problem.

82) Suppose that events E and F are independent, P(E) = 0.9 and P(F ) = 0.4. What is the P(E and F )?

A) 0.94 B) 0.36 C) 1.3 D) 0.036

82)

83) A single die is rolled twice. Find the probability of getting a 5 the first time and a 1 the second time.

Express the probability as a simplified fraction.

A) 1

6 B) 1

12 C) 1

3 D) 1

36

83)

84) You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is

shuffled, and you draw again. Find the probability of getting a picture card the first time and a

spade the second time. Express the probability as a simplified fraction.

A) 3

52 B) 1

13 C) 1

4 D) 3

13

84)

14

85) If you toss a fair coin 10 times, what is the probability of getting all heads? Express the probability

as a simplified fraction.

A) 1

2 B) 1

2048 C) 1

1024 D) 1

512

85)

86) A human gene carries a certain disease from the mother to the child with a probability rate of 51%.

That is, there is a 51% chance that the child becomes infected with the disease. Suppose a female

carrier of the gene has four children. Assume that the infections of the four children are

independent of one another. Find the probability that all four of the children get the disease from

their mother. Round to the nearest thousandth.

A) 0.06 B) 0.058 C) 0.068 D) 0.932

86)

87) A machine has four components, A, B, C, and D, set up in such a manner that all four parts must

work for the machine to work properly. Assume the probability of one part working does not

depend on the functionality of any of the other parts. Also assume that the probabilities of the

individual parts working are P(A) = P(B) = 0.92, P(C) = 0.9, and P(D) = 0.93. Find the probability

that the machine works properly. Round to the nearest ten-thousandth.

A) 0.7618 B) 0.7084 C) 0.77 D) 0.2916

87)

88) Suppose a basketball player is an excellent free throw shooter and makes 94% of his free throws

(i.e., he has a 94% chance of making a single free throw). Assume that free throw shots are

independent of one another. Suppose this player gets to shoot three free throws. Find the

probability that he misses all three consecutive free throws. Round to the nearest ten-thousandth.

A) 0.1694 B) 0.0002 C) 0.8306 D) 0.9998

88)

89) What is the probability that in three consecutive rolls of two fair dice, a person gets a total of 7,

followed by a total of 11, followed by a total of 7? Round to the nearest ten-thousandth.

A) 0.2876 B) 0.0012 C) 0.0015 D) 0.1667

89)

90) A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooded balls. A ball is selected

from the bag, its color noted, then replaced. You then draw a second ball, note its color and then

replace the ball. What is the probability of selecting 2 red balls? Round to the nearest

ten-thousandth.

A) 0.0624 B) 0.0676 C) 0.2600 D) 0.5200

90)

91) A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooded balls. A ball is selected

from the bag, its color noted, then replaced. You then draw a second ball, note its color and then

replace the ball. What is the probability of selecting one white ball and one blue ball? Round to the

nearest ten-thousandth.

A) 0.0088 B) 0.4400 C) 0.2200 D) 0.0480

91)

15

Select the appropriate distribution.

92) Select the distribution that appears to be closest to normal.

A)

B)

C)

D) None of the distributions appear to be normal or near-normal.

92)

16

93) Select the distribution that appears to be closest to normal.

A)

B)

C)

D) None of the distributions appear to be normal or near-normal.

93)

17

94) Select the distribution that appears to be closest to normal.

A)

B)

C)

D) None of the distributions appear to be normal or near-normal.

94)

18

95) Select the distribution that appears to be closest to normal.

A)

B)

C)

D) None of the distributions appear to be normal or near-normal.

95)

Provide an appropriate response.

96) Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a

graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs

would

A) Have the same height but one would be shifted 4 units to the right.

B) Have no horizontal displacement but one would be steeper that the other.

C) Have no horizontal displacement but one would be flatter than the other.

D) Have the same height but one would be shifter 4 units to the left.

96)

97) Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a

graph of a normal density function with mean equal to 0 and standard deviation of 0.5. The graphs

would

A) Have the same height but one would be shifted 4 units to the right.

B) Have no horizontal displacement but one would be steeper that the other.

C) Have no horizontal displacement but one would be flatter than the other.

D) Have the same height but one would be shifter 4 units to the left.

97)

19

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

98) The SAT is an exam used by colleges and universities to evaluate undergraduate

applicants. The test scores are normally distributed. In a recent year, the mean test score

was 1484 and the standard deviation was 298. The test scores of four students selected at

random are 1930, 1340, 2150, and 1450. Find the z-scores that correspond to each value.

98)

99) The ACT is an exam used by colleges and universities to evaluate undergraduate

applicants. The test scores are normally distributed. In a recent year, the mean test score

was 23 and the standard deviation was 5.2. The test scores of four students selected at

random are 16, 24, 9, and 35. Find the z-scores that correspond to each value.

99)

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

Find the probability that a z-score randomly selected from the normal distribution meets the given condition.

100) The z-score is less than 1.5.

A) 0.5199 B) 0.7612 C) 0.0668 D) 0.9332

100)

101) The z-score is less than 1.25.

A) 0.8944 B) 0.7682 C) 0.1056 D) 0.2318

101)

102) The z-score is greater than 1.

A) 0.5398 B) 0.1397 C) 0.8413 D) 0.1587

102)

103) The z-score is greater than -1.25.

A) 0.7193 B) 0.8944 C) 0.5843 D) 0.6978

103)

104) The z-score is between 0 and 3.

A) 0.9987 B) 0.4987 C) 0.4641 D) 0.0010

104)

105) The z-score is between 1 and 2.

A) 0.8413 B) 0.5398 C) 0.2139 D) 0.1359

105)

106) The z-score is between -1.5 and 2.5.

A) 0.6312 B) 0.9270 C) 0.9831 D) 0.7182

106)

107) The z-score is between 1.5 and 2.5.

A) 0.9816 B) 0.0606 C) 0.9938 D) 0.9332

107)

108) The z-score is between -1.25 and 1.25.

A) 0.8817 B) 0.7888 C) 0.6412 D) 0.2112

108)

Provide an appropriate response.

109) A physical fitness association is including the mile run in its secondary-school fitness test. The time

for this event for boys in secondary school is known to possess a normal distribution with a mean

of 440 seconds and a standard deviation of 40 seconds. Find the probability that a randomly

selected boy in secondary school can run the mile in less than 348 seconds.

A) 0.5107 B) 0.4893 C) 0.9893 D) 0.0107

109)

20

110) A physical fitness association is including the mile run in its secondary-school fitness test. The time

for this event for boys in secondary school is known to possess a normal distribution with a mean

of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly

selected boy in secondary school will take longer than 335 seconds to run the mile.

A) 0.9893 B) 0.0107 C) 0.5107 D) 0.4893

110)

111) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the

amount of beer poured by this filling machine follows a normal distribution with a mean of

12.38 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains

fewer than 12.28 ounces of beer.

A) 0.9938 B) 0.0062 C) 0.4938 D) 0.5062

111)

112) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the

amount of beer poured by this filling machine follows a normal distribution with a mean of 10.14

onces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more

than 10.14 ounces of beer.

A) 1 B) 0.4 C) 0.5 D) 0

112)

113) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the

amount of beer poured by this filling machine follows a normal distribution with a mean of

12.29 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains

between 12.19 and 12.25 ounces.

A) 0.1525 B) 0.1649 C) 0.8351 D) 0.8475

113)

114) The length of time it takes college students to find a parking spot in the library parking lot follows a

normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the

probability that a randomly selected college student will find a parking spot in the library parking

lot in less than 4.0 minutes.

A) 0.3085 B) 0.2674 C) 0.1915 D) 0.3551

114)

115) The length of time it takes college students to find a parking spot in the library parking lot follows a

normal distribution with a mean of 6.0 minutes and a standard deviation of 1 minute. Find the

probability that a randomly selected college student will take between 4.5 and 7.0 minutes to find a

parking spot in the library lot.

A) 0.0919 B) 0.4938 C) 0.7745 D) 0.2255

115)

116) The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal

distribution with a mean of 12.06 ounces and a standard deviation of 0.04 ounce. The cans only

hold 12.10 ounces of soda. Every can that has more than 12.10 ounces of soda poured into it causes

a spill and the can needs to go through a special cleaning process before it can be sold. What is the

probability a randomly selected can will need to go through this process?

A) 0.8413 B) 0.3413 C) 0.1587 D) 0.6587

116)

117) A new phone system was installed last year to help reduce the expense of personal calls that were

being made by employees. Before the new system was installed, the amount being spent on

personal calls followed a normal distribution with an average of $600 per month and a standard

deviation of $50 per month. Refer to such expenses as PCE’s (personal call expenses). Using the

distribution above, what is the probability that a randomly selected month had a PCE of between

$475.00 and $690.00?

A) 0.0421 B) 0.0001 C) 0.9579 D) 0.9999

117)

21

118) A new phone system was installed last year to help reduce the expense of personal calls that were

being made by employees. Before the new system was installed, the amount being spent on

personal calls follows a normal distribution with an average of $700 per month and a standard

deviation of $50 per month. Refer to such expenses as PCE’s (personal call expenses). Find the

probability that a randomly selected month had a PCE that falls below $550.

A) 0.0013 B) 0.7857 C) 0.9987 D) 0.2143

118)

119) The tread life of a particular brand of tire is a random variable best described by a normal

distribution with a mean of 60,000 miles and a standard deviation of 2000 miles. What is the

probability a particular tire of this brand will last longer than 58,000 miles?

A) 0.8413 B) 0.2266 C) 0.7266 D) 0.1587

119)

120) The tread life of a particular brand of tire is a random variable best described by a normal

distribution with a mean of 60,000 miles and a standard deviation of 1700 miles. What is the

probability a certain tire of this brand will last between 56,430 miles and 56,940 miles?

A) 0.4649 B) 0.4920 C) 0.9813 D) 0.0180

120)

121) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is

the IQ that corresponds to a z-score of 2.33?

A) 134.95 B) 125.95 C) 142.35 D) 139.55

121)

122) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is

the IQ that corresponds to a z-score of -1.645?

A) 91.0 B) 79.1 C) 82.3 D) 75.3

122)

123) The scores on a mathematics exam have a mean of 66 and a standard deviation of 6. What is the

exam score that corresponds to the z-score -1.645?

A) 64.4 B) 60.0 C) 75.9 D) 56.1

123)

124) Assume that the salaries of elementary school teachers in the United States are normally distributed

with a mean of $40,000 and a standard deviation of $4000. What is the cutoff salary for teachers in

the bottom 10%?

A) $45,120 B) $34,880 C) $33,420 D) $46,580

124)

125) The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard

deviation of 0.95° F. What temperature represents the 95th percentile?

A) 100.16° F B) 100.46° F C) 97.04° F D) 99.82° F

125)

126) A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of

46,900 miles and a standard deviation of 4000 miles. If the manufacturer is willing to replace no

more than 10% of the tires, what should be the approximate number of miles for a warranty?

A) 52,020 B) 53,480 C) 41,780 D) 40,320

126)

127) Compare the scores: a score of 75 on a test with a mean of 65 and a standard deviation of 8 and a

score of 75 on a test with a mean of 70 and a standard deviation of 4.

A) A score of 75 with a mean of 70 and a standard deviation of 4 is better.

B) The two scores are statistically the same.

C) A score of 75 with a mean of 65 and a standard deviation of 8 is better.

D) You cannot determine which score is better from the given information.

127)

22

128) Compare the scores: a score of 88 on a test with a mean of 79 and a score of 78 on a test with a mean

of 70.

A) A score of 75 with a mean of 65 and a standard deviation of 8 is better.

B) You cannot determine which score is better from the given information.

C) The two scores are statistically the same.

D) A score of 75 with a mean of 70 and a standard deviation of 4 is better.

128)

129) Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and a

score of 90 on a test with a mean of 80 and a standard deviation of 8.

A) A score of 90 with a mean of 80 and a standard deviation of 8 is better.

B) A score of 220 with a mean of 200 and a standard deviation of 21 is better.

C) You cannot determine which score is better from the given information.

D) The two scores are statistically the same.

129)

130) Two high school students took equivalent language tests, one in German and one in French. The

student taking the German test, for which the mean was 66 and the standard deviation was 8,

scored an 82, while the student taking the French test, for which the mean was 27 and the standard

deviation was 5, scored a 35. Compare the scores.

A) A score of 35 with a mean of 27 and a standard deviation of 5 is better.

B) The two scores are statistically the same.

C) A score of 82 with a mean of 66 and a standard deviation of 8 is better.

D) You cannot determine which score is better from the given information.

130)

131) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8

and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the

SAT and 25 on the ACT. Compare the scores.

A) A score of 1130 on the SAT test was better.

B) You cannot determine which score is better from the given information.

C) The two scores are statistically the same.

D) A score of 25 on the ACT test was better.

131)

132) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8

and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT

and 16 on the ACT. Compare the scores.

A) A score of 860 on the SAT test was better.

B) A score of 16 on the ACT test was better.

C) You cannot determine which score is better from the given information.

D) The two scores are statistically the same.

132)

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

133) The SAT is an exam used by colleges and universities to evaluate undergraduate

applicants. The test scores are normally distributed. In a recent year, the mean test score

was 1490 and the standard deviation was 292. The test scores of four students selected at

random are 1930, 1340, 2150, and 1450.

a) Find the z-scores that correspond to each value

b) Determine whether any of the values are unusual.

133)

23

134) The ACT is an exam used by colleges and universities to evaluate undergraduate

applicants. The test scores are normally distributed. In a recent year, the mean test score

was 22 and the standard deviation was 5. The test scores of four students selected at random

are 16, 24, 9, and 35.

a) Find the z-scores that correspond to each value.

b) Determine whether any of the values are unusual.

134)

24

Answer Key

Testname: UNTITLED5

1) A

2) A

3) A

4) B

5) B

6) A

7) Answers to parts (a) and (b) will vary.

The answer in part (b) is likely to be closer to the classical probability of 1

4 .

In general, as the number of repetitions of a probability experiment increases, the

closer the empirical probability should get to the classical probability.

8) Answers to parts (a) and (b) will vary.

The answer in part (b) is likely to be closer to the classical probability of 1

4 .

In general, as the number of repetitions of a probability experiment increases, the

closer the empirical probability should get to the classical probability.

9) B

10) C

11) B

12) B

13) C

14) D

15) B

16) B

17) D

18) C

19) D

20) D

21) A

22) A

23) B

24) A

25) C

26) D

27) C

28) 0.215

29) 0.914

30) B

31) D

32) A

33) B

34) C

35) D

36) A

37) C

38) C

39) D

25

Answer Key

Testname: UNTITLED5

40) D

41) D

42) C

43) A

44) B

45) A

46) B

47) B

48) C

49) D

50) B

51) A

52) D

53) B

54) B

55) D

56) B

57) B

58) A

59) C

60) B

61) A

62) C

63) A

64) A

65) D

66) B

67) D

68) D

69) C

70) A

71) A

72) A

73) C

74) D

75) C

76) C

77) B

78) B

79) A

80) B

81) A

82) B

83) D

84) A

85) C

86) C

87) B

88) B

89) C

26

Answer Key

Testname: UNTITLED5

90) B

91) D

92) C

93) A

94) C

95) D

96) A

97) B

98) x = 1930 → z ≈ 1.50

x = 1340 → z ≈ -0.48

x = 2150 → z ≈ 2.23

x = 1450 → z ≈ -0.11

99) x = 16 → z ≈ -1.35

x = 24 → z ≈ 0.19

x = 9 → z ≈ -2.69

x = 35 → z ≈ 2.31

100) D

101) A

102) D

103) B

104) B

105) D

106) B

107) B

108) B

109) D

110) A

111) B

112) C

113) A

114) A

115) C

116) C

117) C

118) A

119) A

120) D

121) A

122) D

123) D

124) B

125) A

126) C

127) B

128) B

129) A

130) C

131) D

132) A

27

Answer Key

Testname: UNTITLED5

133) a) x = 1930 → z ≈ 1.51

x = 1340 → z ≈ -0.51

x = 2150 → z ≈ 2.26

x = 1450 → z ≈ -0.14

b) x = 2150 is unusual because its corresponding z-score (2.26) lies more than 1.96 standard deviations from the mean.

134) a) x = 16 → z ≈ -1.20

x = 24 → z ≈ 0.40

x = 9 → z ≈ -2.60

x = 35 → z ≈ 2.60

b) x = 9 is unusual because its corresponding z-score (-2.60) lies more than 1.96 standard deviations from the mean.

x = 35 is unusual because its corresponding z-score (2.60) lies more than 1.96 standard deviations from the mean.

28

Category: Statistics

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