Probability and Probability Distribution

SECTION - A

1) Which of the following is an example of a random experiment?

A) A customer inspects a delivery and finds an error.

B) Marketing budgets a 10% increase in advertising.

C) The post office misplaces a letter.

D) A student increases her average study time/week and improves her grades.

2) The set of all possible outcomes from a random experiment is called the sample:

A) population.

B) space.

C) probability.

D) event.

3) Which of the following is not an example of a random experiment?

A) daily change of stock market index prices

B) customer makes a purchase or not

C) a survey to rate quality of service

D) coin-toss, heads or tails

4) The possible outcomes from a random experiment are called:

A) sample space.

B) parameters.

C) basic groups.

D) basic outcomes.

5) A subset of outcomes is defined as a(n):

A) sample.

B) event.

C) outcome.

D) probability.

6) When events have no common basic outcomes, they are said to be:

A) mutually exclusive.

B) mutually related.

C) mutually apart.

D) collectively exhaustive.

7) If the union of several events covers the entire sample space, it is said these events are:

A) mutually exclusive.

B) mutually related.

C) mutually apart.

D) collectively exhaustive.

8) The proportion of times that an event will occur, assuming that all outcomes in a sample space are equally likely to occur, is called:

A) objective probability.

B) classical probability.

C) relative frequency probability.

D) subjective probability.

9) ________ probability is the number of events in the population that meet the condition divided by the total number in the population.

A) Objective

B) Classical

C) Relative frequency

D) Subjective

10) The expression of an individual's degree of belief about the chance that an event will occur is called ________ probability.

A) objective

B) classical

C) relative frequency

D) subjective

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

Suppose you roll a pair of dice. Let A be the event that you observe an even number. Let B be the event that you observe a number greater than seven.

11) What is the intersection of events A and B?

A) [8, 10, 12]

B) [7, 8, 9, 10, 11, 12]

C) [2, 4, 6, 8, 10, 12]

D) [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]

12) What is the union of events A and B?

A) [8, 9, 10, 11, 12]

B) [8, 10, 12]

C) [2, 4, 6, 8, 9, 10, 11, 12]

D) [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]

13) What is the complement of event A?

A) [8, 9, 10, 11, 12]

B) [3, 5, 7, 9, 11]

C) [1, 5, 10, 11, 12]

D) [8, 10, 12]

14) What is the complement of event B?

A) [3, 5, 7, 9, 11]

B) [2, 4, 6, 8, 10, 12]

C) [2, 3, 4, 5, 6, 7]

D) [7, 8, 9, 10, 11, 12]

15) What is B?

A) [9, 11]

B) [2, 3, 4, 6]

C) [5, 7, 8, 10, 12]

D) [3, 5]

16) What is A ?

A) [9, 11]

B) [8, 10, 12]

C) [3, 5, 7]

D) [2, 4, 6]

17) What is ?

A) [2, 4, 6]

B) [3, 5, 7]

C) [8, 9, 10, 11, 12]

D) []

18) What is ?

A) [2, 3, 4, 5, 6, 7]

B) [3, 5, 7]

C) [2, 3, 4, 5, 6, 7, 9, 11]

D) [2, 4, 6]

19) What is B?

A) [4, 5, 7, 8, 11, 12]

B) [8, 9, 10, 11, 12]

C) [2, 3, 4, 5, 6, 7]

D) [3, 5, 7, 8, 9, 10, 11, 12]

20) What is A ?

A) [2, 3, 4, 5, 6, 7, 8, 10, 12]

B) [3, 5, 7, 8, 10, 12]

C) [5, 7, 8, 10, 12]

D) [5, 6, 7, 8, 9, 10, 11, 12]

21) What does the complement rule state?

A) That events A and are not mutually exclusive

B) The intersection of events A and is the empty set .

C) That events A and are not collectively exhaustive.

D) The union of events A and is the empty set .

22) The probability of the intersection of events A and B is denoted by:

A) A B.

B) P(A B).

C) A B.

D) P(A B).

23) If the probability of occurrence of event A is not affected by the occurrence of event B, then A and B are said to be:

A) mutually exclusive.

B) statistically independent.

C) collectively exhaustive.

D) basic events.

24) Suppose you roll a pair of dice. Let A be the event that you roll an even number. Let B be the event that you roll an odd number. Which of the following statements is true?

A) The events A and B are not mutually exclusive.

B) The intersection of A and B is the empty set .

C) The events A and B are not collectively exhaustive.

D) The complement of event B is the set [1, 3, 5, 7, 9, 11].

25) Which of the following statements is always true for any two events A and B defined on a sample space S?

A) The complement of event A is event B.

B) The intersection of A and B is the set of all basic outcomes in either A or B.

C) If events A and B are mutually exclusive, then A B = S.

D) If events A and B are collectively exhaustive, then A B = S.

26) Which of the following statements is always true for any two events A and B defined on a sample space S?

A) If the complement of event A is the empty set, then event A is the sample space S.

B) If the union of events A and B is not the empty set, then A B = .

C) If events A and B are mutually exclusive, then A B = S.

D) If events A and B are collectively exhaustive, then A B = .

27) Which of the following statements is true for any two events A and B defined on a sample space S?

A) If the intersection of events A and B is the empty set, then A and B are collectively exhaustive.

B) If the union of events A and B is the empty set, then each of A and B is the empty set.

C) If events A and B are collectively exhaustive, then A B .

D) If events A and B are mutually exclusive and collectively exhaustive, then the union of A and B is not necessarily the sample space.

28) Which term is used to describe the probability of the intersection of events A and B?

A) subjective probability

B) marginal probability

C) joint probability

D) conditional probability

29) Two events A and B defined on a sample space S are said to be collectively exhaustive if:

A) A B =

B) A B =

C) A B = S

D) A B = S

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

The production manager at a local manufacturing plant is concerned about work stoppages in the four production lines. In particular, the manager is evaluating the likelihood of the next stoppage occurring on production line 1.

30) If each of the lines is equally likely to have the next stoppage, the probability that production line 1 is stopped next is 25%. This is an example of:

A) subjective probability.

B) classical probability.

C) relative frequency probability.

D) Bayesian probability.

31) Based on previous stoppage records, the manager figures that the probability that production line 1 is stopped next is 25%. This is an example of:

A) subjective probability.

B) classical probability.

C) relative frequency probability.

D) Bayesian probability.

32) Based on his knowledge of the causes of stoppages, the manager states that the probability that production line 1 is stopped next is 25%. This is an example of:

A) subjective probability.

B) classical probability.

C) relative frequency probability.

D) Bayesian probability.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

In a furniture manufacturing plant, a customer survey indicates that blemishes in the finish are a major concern. The table shown below displays a quality manager's probability assessment of the number of defects in the finish of new furniture.

Number of Defects

0

1

2

3

4

5

Probability

0.34

0.25

0.19

0.11

0.07

0.04

33) Let event A be that there are more than three defects and let event B be that there are four or fewer defects. Which of the following statements is true?

A) P(A B) = 0.18

B) P(A B) = 0.07

C) Events A and B are collectively exhaustive.

D) Events A and B are mutually exclusive.

34) Let event A be that there are more than two defects and let event B be that there are four or fewer defects. Which of the following statements is true?

A) P(A B) = 0.18

B) P(A B) = 0.07

C) P( ) = 0.58

D) P( ) = 0.89

35) Let A be the event that there is at least one defect and let event B be that there is at most three defects. Which of the following statements is true?

A) P(A B) = 0.55

B) P(A B) = 0.96

C) P(A) = 0.34

D) P( ) = 0.89

36) A gumball machine has five different colored gumballs: red, blue, white, green, and yellow. If you buy three gumballs, how many different combinations of colors could you buy?

A) 60

B) 20

C) 10

D) 6

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

Ted's Surfboard Shop makes surfboards by hand. The number of surfboards that Ted makes in a week depends on the wave conditions. Ted has estimated the following probabilities for surfboard production for the next week.

Number of Surfboards

5

6

7

8

9

10

Probability

0.13

0.22

0.31

0.17

0.13

0.04

37) Let event A be that Ted produces more than seven surfboards and let event B be that he produces exactly six surfboards. Which of the following statements is true?

A) P(A B)=0.31

B) events A and B are collectively exhaustive

C) P( )=0.44

D) events A and B are mutually exclusive

38) Let event A be that Ted produces more than six surfboards, and let event B be that he produces less than eight surfboards. Which of the following statements is true?

A) P(A B) = 0.75

B) Events A and B are collectively exhaustive.

C) P( ) = 0.53

D) Events A and B are mutually exclusive.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

The probability that interest rates on housing loans will go up in the next 6 months is estimated to be 0.20. The probability that house sales will decrease is estimated to be 0.6. The probability that interest rates will go up and house sales will decrease is estimated to be 0.15.

39) The probability that interest rates increase and house sales decrease is:

A) 0.75

B) 0.85

C) 0.71

D) 0.15

40) The probability of an increase in interest rates and not a decrease in house sales is:

A) 0.20

B) 0.05

C) 0.25

D) 0.50

41) The probability of a decrease in house sales and not an increase in interest rates is:

A) 0.45

B) 0.25

C) 0.20

D) 0.05

42) The probability of not an increase in interest rates and not a decrease in house sales is:

A) 0.50

B) 0.35

C) 0.20

D) 0.05

43) The probability that house sales will go down given that interest rates will go up is:

A) 0.95

B) 0.90

C) 0.75

D) 0.80

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A multiple choice quiz has five questions, each with five answers, A through E. Assume you just guess on all of the questions.

44) What is the probability that you guessed on all five questions right?

A) 0.00032

B) 0.03125

C) 0.20

D) 0.50

45) What is the probability that you get exactly three questions right?

A) 0.00032

B) 0.0016

C) 0.008

D) 0.04

46) A research project on retention at a large university indicated that 20% of the students had a problem with stress while 25% reported problems with financial resources and 15% had a problem with both. What is the probability that a particular student has a problem with either stress or financial resources?

A) 0.15

B) 0.30

C) 0.45

D) 0.60

47) The probability that an employee at a company uses illegal drugs is 0.08. The probability than an employee is male is 0.55. Assuming that these events are independent, what is the probability that a randomly chosen employee is a male drug user?

A) 0.742

B) 0.145

C) 0.044

D) 0.006

48) A survey of executives revealed that 35% of them regularly read The Wall Street Journal, 20% read Forbes, and 10% read both The Wall Street Journal and Forbes. What is the probability that a particular executive reads either The Wall Street Journal or Forbes?

A) 0.45

B) 0.35

C) 0.55

D) 0.65

49) In a longitudinal economic development study, market research indicated that the odds of a new business succeeding after five years are 1 to 9. That means that the probability of a business actually succeeding is:

A) 0.11

B) 0.10

C) 0.09

D) 0.08

50) A junior executive looking at his business attire in his closet notes that he has five suits, six shirts, and three pairs of shoes. He is going on a business trip and needs to take two of each. How many different combinations of outfits could he take?

A) 680

B) 320

C) 450

D) 224

SECTION - B

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A recent marketing survey related consumers' awareness of a new marketing campaign with their rating of the product. Consumers rated their awareness as low, medium, or high, and rated the product as poor, fair, or good. The results are presented below.

51) What is the probability that a consumer had low awareness?

A) 0.10

B) 0.14

C) 0.23

D) 0.07

52) What is the probability that a consumer who ranked the product as fair had a high awareness of the ad campaign?

A) 0.06

B) 0.26

C) 0.23

D) 0.40

Answer:B

53) What is the probability that a consumer who had high awareness of the ad campaign ranked the product as good?

A) 0.675

B) 0.385

C) 0.775

D) 0.325

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A manufacturer of automobiles conducted a market survey. Eighty percent of the customers want better fuel efficiency, while 55% want a vehicle navigation system and 45% percent want both features.

54) The probability that a person wants better fuel efficiency and also a vehicle navigation system is:

A) 0.90

B) 0.10

C) 0.45

D) 0.35

55) The probability that a person wants better fuel efficiency but not a vehicle navigation system is:

A) 0.90

B) 0.10

C) 0.45

D) 0.35

56) The probability that a person wants a vehicle navigation system but not better fuel efficiency is:

A) 0.90

B) 0.10

C) 0.45

D) 0.35

57) The probability that a person wants neither better fuel efficiency nor a vehicle navigation system is:

A) 0.90

B) 0.10

C) 0.45

D) 0.35

58) The probability that a person wants either better fuel efficiency or a vehicle navigation system is:

A) 0.90

B) 0.10

C) 0.45

D) 0.35

59) The probability that a person does not want a vehicle navigation system is:

A) 0.45

B) 0.10

C) 0.90

D) 0.35

60) The probability that a person wants a better fuel efficiency given that he wants a vehicle navigation system is approximately:

A) 0.90

B) 0.45

C) 0.82

D) 0.41

61) The probability that a person wants a vehicle navigation system given that he wants a better fuel efficiency is approximately:

A) 0.80

B) 0.40

C) 0.45

D) 0.56

62) A junior executive looking at his business attire in his closet notes that he has eight suits, six shirts, and four pairs of shoes. He is going on a business trip and needs to take two of each. How many different combinations of outfits could he take?

A) 2240

B) 3320

C) 1680

D) 2520

63) The purchasing agent for a municipality has contracted with a local car dealer to purchase four cars. The dealer has 25 cars on his lot; 10 red, 7 blue, 6 white, and 2 purple. If the purchasing agent has no control over the colors he receives, what is the probability that he receives at least one of the purple cars?

A) 0.33

B) 0.30

C) 0.36

D) 0.39

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A recent survey showed that 15% of computer programmers have experienced some form of wrist pain from typing, and that 25% are taking aspirin daily. Six percent of all programmers have both experienced some form of wrist pain from typing and taken aspirin on a daily basis.

64) What is the probability that a programmer who has wrist pain takes aspirin on a daily basis?

A) 0.40

B) 0.24

C) 0.57

D) 0.66

65) What is the probability that a programmer who takes aspirin on a daily basis has wrist pain?

A) 0.09

B) 0.19

C) 0.24

D) 0.40

66) What is the probability that a programmer has wrist pain and does not take aspirin on a daily basis?

A) 0.25

B) 0.15

C) 0.19

D) 0.09

67) What is the probability that a programmer does not have wrist pain and does not take aspirin on a daily basis?

A) 0.75

B) 0.66

C) 0.85

D) 0.25

68) What is the probability that a programmer has wrist pain or takes aspirin on a daily basis?

A) 0.66

B) 0.25

C) 0.34

D) 0.15

69) As the office manager for a medical office with ten doctors, you are responsible for developing the roster for the on-call shift for the next three nights. How many different ways could you assign a different doctor to each of the next three nights?

A) 1020

B) 840

C) 720

D) 640

70) Which of the following statements is true?

A) If events A and B are complements, then the intersection of A and the complement of B is the sample space.

B) If events A and B are mutually exclusive, then the intersection of A and B is the empty set.

C) If events A and B are mutually exclusive, then the union of A and B is the sample space.

D) If events A and B are mutually exclusive, then the union of A and B is the empty set.

71) In a recent article it was reported that 35.4% of all high school students smoke cigarettes. 65% of these students plan on going to college. What is the probability that a randomly selected student smokes cigarettes and plans on going to college?

A) 0.354

B) 0.230

C) 0.124

D) 0.412

72) An office of six people is plagued by high absenteeism. It is thought that the probability that an employee is absent on a particular day is 0.03. Assuming that the event that one person is absent on a particular day is independent of the absence of any other employee, what is the probability that at least one employee is absent tomorrow?

A) 0.121

B) 0.180

C) 0.150

D) 0.167

73) A gumball machine has six red gumballs, four blue gumballs, and three yellow gumballs. If you buy three gumballs, what is the probability that you get three different colors?

A) 0.252

B) 0.167

C) 0.125

D) 0.244

Answer:A

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A survey of recent e-commerce start-up firms was undertaken at an industry convention. Representatives of the firm were asked for the geographic location of the firm as well as the firm's outlook for growth in the coming year. The results are provided below.

74) What is the probability that one of these start-up firms was from the Northeast?

A) 0.04

B) 0.12

C) 0.49

D) 0.33

75) Are the events "firm from the South" and "expects high growth" statistically independent?

A) Yes

B) No

C) Maybe

D) Unable to tell from the data

76) If the firm interviewed was from the West, what is the probability that it expected medium or high growth?

A) 0.24

B) 0.35

C) 0.16

D) 0.46

77) If the firm interviewed was expecting medium or high growth, what is the probability of the firm being located in the West?

A) 0.16

B) 0.31

C) 0.46

D) 0.27

78) In a survey of 100 large corporations, it was found that 72% offer some form of tuition assistance plan for their workers. 64% of the 100 corporations offer both a tuition assistance plan as well as provide dental insurance for dependents. What is the probability that a corporation that offers a tuition assistance plan also offers dental insurance for dependents?

A) 0.89

B) 0.46

C) 0.64

D) 0.68

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A supplier is evaluating a firm to manufacture a subassembly. Quality data from past inspections reveal the following probabilities for number of defective parts in a shipment:

Number Defective

0

1

2

>2

Probability

0.80

0.10

0.06

0.04

79) What is the probability that there will be fewer than 2 defective parts in a shipment?

A) 0.20

B) 0.90

C) 0.86

D) 0.10

80) What is the probability that the shipment will have defective parts?

A) 0.20

B) 0.90

C) 0.86

D) 0.10

81) What is the probability that the shipment will have at least two defective parts?

A) 0.20

B) 0.90

C) 0.86

D) 0.10

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

In a recent survey of consumer confidence, 160 respondents were classified by their level of education. The results of the survey are presented below.

82) What is the proportion of respondents who had medium or high confidence?

A) 0.330

B) 0.271

C) 0.719

D) 0.670

83) What proportion of respondents had at least some college education and had high confidence?

A) 0.131

B) 0.242

C) 0.558

D) 0.175

84) What proportion of respondents who had at least some college education also had high confidence?

A) 0.239

B) 0.210

C) 0.364

D) 0.636

85) Are the events "had a college education" and "had high confidence" statistically independent?

A) Yes

B) No

C) Maybe

D) There is not sufficient information to determine.

86) If the odds for you getting a credit card solicitation in the mail this month are 1 to 4, then which of the following statements is true?

A) The probability of getting a credit card solicitation is 0.25.

B) The probability of getting a credit card solicitation is 0.20.

C) The probability of getting a credit card solicitation is 0.80.

D) The probability of getting a credit card solicitation is 0.75.

87) Consider two events A and B. Which of the following statements is true?

A) If the probability of A given B is 0.4, then the probability of A given the complement of B is 0.6.

B) If the probability of A given B is 0.4, then the probability of the complement of A given the complement of B is 0.6.

C) If the probability of A given B is 0.4, then the probability of the complement of A given B is 0.6

D) If the probability of A given B is 0.4 and the probability of A is 0.4, then events A and B are mutually exclusive.

88) If P(A) = 0.20, P(B) = 0.40, and P(A B) = 0.08, then A and B are said to be:

A) dependent events.

B) independent events.

C) mutually exclusive events.

D) complementary events.

89) Two events A and B are said to be mutually exclusive if:

A) P(A | B) = 1

B) P(B | A) = 1

C) P(A B) = 1

D) P(A B) = 0

90) If P(A) = 0.84, P(B) = 0.76, and P(A B) = 0.90, then P(A B) is:

A) 0.06

B) 0.14

C) 0.70

D) 0.83

91) The diagram which provides an intuitive understanding of the addition rule which computes the probability of the union of events is called a:

A) plot diagram.

B) scattered diagram.

C) Venn diagram.

D) tree diagram.

92) Events whose probability of their intersection is the product of their individual probabilities and is more than 0 are called:

A) mutually exclusive.

B) complement.

C) conditional.

D) independent.

93) The application which provides a way of revising conditional probabilities by using available information and provisions for revising conditional probabilities with other information that is useful for management decision making is called:

A) overinvolvement ratios.

B) Bayes' theorem.

C) empirical formula.

D) probability rules.

94) There are five men and four women working on a project. To handle one particular aspect of the project, a subcommittee needs to be formed. In the interest of balance, it is decided that the subcommittee will consist of two men and two women. How many combinations of this subcommittee are possible?

95) The probability that an employee at a company eats lunch at the company cafeteria is 0.32. The probability that an employee is female is 0.62. The probability than an employee eats lunch at the employee cafeteria and is female is 0.21. What is the probability that a randomly chosen employee either eats at the cafeteria or is female?

96) In a recent article it was reported that 27.3% of all college students party during weekdays, and 67% of these students plan on going to graduate school. What is the probability that a randomly-selected student party during weekdays and plans on going to graduate school?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A student has access to professor evaluations. Overall, he has enjoyed 70% of all classes he has taken. He finds that of the courses he has enjoyed, 13% were taught by professors with poor evaluations. 84% of the courses he has taken were taught by professors with good evaluations.

97) What is the probability that the class was taught by a professor with poor evaluations and that the student enjoyed the class?

98) What is the probability that the class was taught by a professor with good evaluations and that the student enjoyed the class?

99) What is the probability that the student enjoyed the class given that it was taught by a professor with good evaluations?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

In a recent survey about US policy in Iraq, 62 % of the respondents said that they support US policy in Iraq. Females comprised 53% of the sample, and of the females, 46% supported US policy in Iraq. A person is selected at random.

100) What is the probability that the person we select is female and supports U.S. policy in Iraq?

101) Are the events "does not support U.S, policy in Iraq" and "female" statistically independent? Why or why not?

102) What is the probability that the person we select is male?

103) What is the probability that the person we select does not support US policy in Iraq?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

James' Surfboard Shop makes surfboards by hand. The number of surfboards that James makes during a week depends on the wave conditions. James has estimated the following probabilities for surfboard production for the next week.

Number of Surfboards

5

6

7

8

9

10

Probability

0.13

0.22

0.31

0.17

0.13

0.04

Let A be the event that James produces more than seven surfboards. Let B be the event that James produces exactly six surfboards.

104) What is the probability of event A?

105) What is the probability of the complement of A?

106) What is the probability of the intersection of events A and B? Why?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A recent marketing survey tried to relate a consumer's awareness of a new marketing campaign with their rating of the product. Consumers rated their awareness as low, medium, or high, and rated the product as poor, fair, or good. The results are presented below.

107) What is the probability that a consumer had both high awareness and thought the product was poor?

108) What is the probability that a consumer who had medium awareness ranked the product as fair or good?

109) What is the probability that a consumer who did not rank the product as poor had high awareness?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A review of the personnel records of a small corporation has revealed the following information about the number of sick days taken per year and the corresponding probabilities.

Number of Sick Days

0

1

2

3

4

5

Probability

0.05

0.22

0.31

0.27

0.13

0.02

Let A be the event that an employee takes more than 2 sick days. Let B be the event that an employee takes less than five sick days.

110) What is the probability of event A?

111) Are events A and B collectively exhaustive? Why?

112) What is the probability of the intersection of events A and B?

113) Are events A and B mutually exclusive? Why?

114) The probability that a new small business closes before the end of its first year is 42%. In addition, 37% of all new businesses are started by women. The probability that a new business is either owned by a woman or goes out of business is 62%. Your sister starts a new business. What is the probability her business will still open at the end of the first year?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

A company wishes to evaluate the effectiveness of a marketing campaign. Seventy five percent of all potential professors were reached in a focused advertising program. Twenty eight percent of those contacted adopted the book while 8% of the adoptions came from professors who did not receive the promotional material. Define the following events of interest:

A1= Professor received advertising material

A2= Professor did not receive advertising material

B1= Professor adopts the book

B2= Professor does not adopt the book

115) What is the probability that a professor who adopts the book received the advertising material?

116) What is the probability that a professor who adopts the book has not received the advertising material?

117) What is the probability that a professor who received advertising material does not adopt the book?

118) What is the probability that a professor who does not receive advertising material has not adopted the book?

119) What is the probability that a professor received advertising material and adopts the book?

120) What is the probability that a professor received advertising material and does not adopt the book?

121) A variable that can take on a finite and countable number of values is a ________ variable.

A) qualitative

B) discrete

C) continuous

D) Poisson

122) Which of the following is true about a probability distribution?

A) The sum of all possible outcomes must not equal 1.

B) The representation must be graphed, not tabular or algebraic.

C) The probability of each outcome must be between 0 and 1, inclusive.

D) The outcomes do not need to be mutually exclusive.

123) A random variable which takes on no more than a countable number of values is called a(n):

A) continuous random variable.

B) outcome.

C) statistic.

D) discrete random variable.

124) The expected value of a random variable, denoted , is also called its:

A) mode.

B) median.

C) mean.

D) variance.

125) The standard deviation of a discrete random variable is the positive square root of its:

A) variance.

B) mean.

C) median.

D) mode.

126) The approach, to develop the binomial probability distribution, begins with the:

A) Bayes' theorem.

B) Empirical rule.

C) Venn diagram.

D) Bernoulli model.

127) The Poisson distribution can be used to approximate the binomial probabilities when the number of trials n is large and at the same time the probability P is:

A) also large.

B) one.

C) small.

D) equal to .

SECTION - C

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

The probability that a person catches a cold during the cold and flu season is 0.4. Assume that 10 people are chosen at random.

128) What is the probability that exactly four of them will catch a cold?

A) 0.7502

B) 0.6330

C) 0.3670

D) 0.2508

129) What is the probability that four or more of them will catch a cold?

A) 0.715

B) 0.618

C) 0.546

D) 0.312

130) On average, how many of these ten people would you expect to catch a cold?

A) 4

B) 3

C) 2

D) 1

131) What is the standard deviation for the number of people catching a cold?

A) 1.549

B) 1.245

C) 1.265

D) 1.125

132) Which of the following can be used to approximate the binomial distribution when the number of trials n is large and the probability of success P is small such that nP 7?

A) Poisson distribution

B) hypergeometric distribution

C) any discrete distribution

D) any distribution with a mean equals 7

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

On average, you receive 2.6 pieces of junk mail a day. Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution.

133) What is the probability that you receive exactly three pieces of junk mail today?

A) 0.198

B) 0.233

C) 0.218

D) 0.176

134) What is the probability of receiving more than three pieces of junk mail today?

A) 0.123

B) 0.264

C) 0.482

D) 0.242

135) What is the standard deviation of the number of pieces of junk mail you receive daily?

A) 1.61

B) 2.60

C) 6.76

D) There is not sufficient information to determine this.

136) What is the expected number of pieces of junk mail you receive daily?

A) 6.76

B) 1.61

C) 3.22

D) 2.60

137) Consider the following probability distribution. Which of the following is true?

x

0

1

2

3

4

5

6

7

P(x)

0.05

0.16

0.19

0.24

0.18

0.11

0.05

0.02

A) P(2 < X < 5) = 0.42

B) P(X > 6) = 0.07

C) P(X 3) = 0.64

D) P(X 6) = 0.93

138) If the outcomes of a discrete random variable follow a Poisson distribution, then their:

A) mean equals the standard deviation.

B) mean equals the variance.

C) median equals the variance.

D) median equals the standard deviation.

139) Which of the following is an example of a discrete random variable?

A) The distance you can drive in a car with a full tank of gas.

B) The number of cows on a cattle ranch.

C) The weight of a package at the post office.

D) The amount of rain that falls over a 24-hour period.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

A company hires management trainees for entry level sales positions. Past experience indicates that only 10% will still be employed at the end of nine months. Assume the company recently hired six trainees.

140) What is the probability that three of the trainees will still be employed at the end of nine months?

A) 0.0012

B) 0.0146

C) 0.0415

D) 0.0446

141) What is the probability that at least two of the trainees will still be employed at the end of nine months?

A) 0.9841

B) 0.0984

C) 0.1143

D) 0.0159

142) What is the probability that none of the trainees will still be employed at the end of nine months?

A) 0.5314

B) 0.3771

C) 0.4686

D) 0.0000

143) What is the probability that between one and three (inclusive) of the trainees will still be employed at the end of nine months?

A) 0.3543

B) 0.0984

C) 0.0146

D) 0.4673

144) What is the expected number of the trainees that will still be employed at the end of nine months?

A) 0.6

B) 0.9

C) 3.0

D) 4.0

145) What is the standard deviation of the number of trainees that will still be employed at the end of nine months?

A) 0.540

B) 0.240

C) 0.735

D) 0.490

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

On average, there are 3.2 defects in a sheet of rolled steel. Assume that the number of defects follows a Poisson distribution.

146) What is the probability of having exactly three defects in a roll?

A) 0.412

B) 0.223

C) 0.318

D) 0.335

147) What is the probability of having more than three defects in a roll?

A) 0.354

B) 0.398

C) 0.412

D) 0.621

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

A basketball player makes 80 percent of his free throws during the regular season. Consider his next eight free throws.

148) What is the probability that he will make exactly six free throws?

A) 0.1468

B) 0.3355

C) 0.1678

D) 0.2936

149) What is the probability that he will make at least six free throws?

A) 0.1468

B) 0.3355

C) 0.7969

D) 0.2936

150) What is the probability that he will make between four and six (inclusive) free throws?

A) 0.1468

B) 0.4863

C) 0.4404

D) 0.6291

151) What is the expected number of free throws that he will make?

A) 6.4

B) 6.0

C) 5.0

D) 4.0

152) What is the standard deviation of the number of free throws that he will make?

A) 1.131

B) 1.280

C) 2.608

D) 2.828

153) The finishing process on new furniture leaves slight blemishes. The table below displays a manager's probability assessment of the number of blemishes in the finish of new furniture.

Number of Blemishes

0

1

2

3

4

5

Probability

0.34

0.25

0.19

0.11

0.07

0.04

On average, how many defects would we expect on a piece of furniture?

A) 0.28

B) 0.85

C) 1.44

D) 0.77

154) Thirty percent of all households have a DVD player. If you select 20 houses at random, what is the probability that six or fewer of them have a DVD player?

A) 0.608

B) 0.416

C) 0.344

D) 0.238

155) The number of rainy days per month at Seattle follows a Poisson distribution with a mean value of 4.5 days. What is the probability that it will rain 3 days next month?

A) 0.3604

B) 0.2222

C) 0.1687

D) 0.2521

156) The sum of the product of each value of a discrete random variable X and its probability is referred to as its:

A) probability distribution.

B) expected value.

C) variance.

D) standard deviation.

157) Consider the following probability distribution. Which of the following is true?

x

0

1

2

3

4

5

6

P(x)

0.07

0.19

0.23

0.17

0.16

0.14

0.04

A) P(X > 3) = 0.51

B) P(2 X 5) = 0.33

C) P(X 3) = 0.51

D) P(X < 6) =1

158) The number of orders shipped to a supplier that are inaccurate each month is an example of a:

A) discrete variable.

B) continuous variable.

C) binary variable.

D) hypergeometric variable.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

A cereal manufacturer produces a cereal that claims to contain 16 ounces in each box. A sample of boxes results in the following table.

Weight in Ounces

14

15

16

17

Probability

0.10

0.30

0.40

0.20

159) What is the mean weight of the sample of cereal boxes?

A) 15.5

B) 15.7

C) 16.0

D) 16.5

160) What is the standard deviation of the weight of cereal in the boxes?

A) 0.81

B) 1.25

C) 0.90

D) 1.19

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

Consider the following probability distribution function.

x

0

1

2

3

4

5

6

P(x)

0.07

0.19

0.23

0.17

0.16

0.14

0.04

161) What is the expected value of X?

A) 2.74

B) 0.46

C) 1.78

D) 3.02

162) What is the standard deviation of X?

A) 13.25

B) 3.64

C) 1.62

D) 4.13

163) Which of the following is true for the binomial distribution?

A) There are at least three or more possible outcomes.

B) The probability of success remains the same for each trial.

C) The probability of success P, is equal to 1.99 most of the time.

D) The number of trials are not independent.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes. Assume that the number of calls follows the Poisson distribution.

164) What is the probability that there are three or fewer calls during the next ten minutes?

A) 0.211

B) 0.372

C) 0.396

D) 0.425

165) What is the probability that there are exactly four calls during the next ten minutes?

A) 0.194

B) 0.172

C) 0.156

D) 0.134

166) It has been estimated that 30% of all farms are family-owned. In a sample of 12 farms, what is the probability that exactly three farms are family owned?

A) 0.20

B) 0.30

C) 0.36

D) 0.24

167) chocolates, there are four chocolates with coconut filling. What is the probability of choosing four chocolates, none of which have coconut fillings?

A) 0.272

B) 0.264

C) 0.248

D) 0.236

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

The number of accidents on a particular highway averages 4.4 per year. Assume that the number of accidents follows a Poisson distribution.

168) What is the probability that there are exactly four accidents next year?

A) 0.504

B) 0.192

C) 0.375

D) 0.286

169) What is the probability that there are more than three accidents next year?

A) 0.389

B) 0.440

C) 0.512

D) 0.641

170) A recent survey showed that 5 percent of the computer keyboards produced by a particular company are defective. What is the probability that out of eight keyboards selected at random, exactly zero keyboards will be defective?

A) 0.0054

B) 0.2793

C) 0.6634

D) 0.6983

171) There are 15 professors in the School of Education. Twelve of them have received good evaluations from students, while 3 received poor evaluations. You will take three courses in the School of Education next semester. What is the probability that all of your professors next semester have received good evaluations?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

A recent survey found that 40% of all air traffic controllers found their job extremely stressful. Suppose 12 air traffic controllers are selected at random.

172) What is the probability that exactly 5 of them consider their job extremely stressful?

A) 0.241

B) 0.213

C) 0.227

D) 0.232

173) What is the probability that two or more of them consider their job extremely stressful?

A) 0.7218

B) 0.9804

C) 0.0282

D) 0.2806

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.

# of claims

2

3

4

5

6

7

P(x)

0.11

0.16

0.27

0.23

0.13

0.10

174) What is the average number of claims processed?

A) 4.67

B) 4.23

C) 4.41

D) 4.81

175) What is the variance of the number of claims processed?

A) 3.6211

B) 2.0819

C) 1.4428

D) 1.9029

176) Which of the following is true?

A) P(X > 4) = 0.46

B) P(X 4) = 0.27

C) P(X > 2) = 1.00

D) P(X 6) = 0.10

177) There is a 50% chance that a newborn baby will be a boy. For families with four children, what is the probability that all the children are boys?

A) 0.2512

B) 0.3754

C) 0.0625

D) 0.1587

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

70% of the customers at the local ice cream shop order their ice cream on a sugar cone. Assume that the next ten customers order independently of one another.

178) What is the probability that more than half of them order sugar cones?

A) 0.95

B) 0.85

C) 0.05

D) 0.15

179) What is the probability that exactly seven of them order sugar cones?

A) 0.2668

B) 0.5000

C) 0.6500

D) 0.3500

180) Which of the following is an example of a binomial experiment?

A) A shopping mall is interested in the income level of its customers and is taking a survey to gather information.

B) A business firm introducing a new product wants to know how many purchases its clients will make each year.

C) A sociologist is researching an area in an effort to determine the proportion of households with a male head of household.

D) A study is concerned with the average number of hours worked by high school students.

181) Given a Poisson random variable X, where the average number of times an event occurs in a certain period of time is 2.5, then P(X = 0) is:

A) 2.5

B) 0.0821

C) 1.5811

D) 0.40

182) If X and Y are random variables, the sum of all the conditional probabilities of X given a specific value of Y will always be:

A) the average of the possible values of X.

B) the average of the possible values of Y.

C) 1.

D) 0.

SECTION - D

183) Suppose you know that the number of complaints coming into a phone center averages 3 every ten minutes. Assume that the number of calls follows the Poisson distribution. What is the probability that there are exactly three calls during the next ten minutes?

184) An auditor reviewing the invoices of a small company finds that there are errors in 1.5% of them. If the auditor looks at 500 invoices, what is the probability that he finds more than 3 invoices with errors? Use the Poisson approximation to the binomial distribution.

185) The number of accidents on a US -131 highway average 4.4 per year. Assuming that the number of accidents follows a Poisson distribution, what is the probability that there are more than three accidents next year on US - 131?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

As a purchasing agent, you are responsible for selecting sources of supply for manufactured components to use in your firm's production process. The salesman for a certain supplier has indicated that they can supply an electronic sub-assembly that has a defect rate of 1.1%-well below your current supplier's defect rate. You accept 100 sub-assemblies for evaluation, and find that there were four defects.

186) Using the Poisson approximation to the binomial, how likely is it to get four or less defects out of 100?

187) Using the Poisson approximation to the binomial, how likely is it to get exactly four defects out of 100?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

It has been reported that 1.7% of the work force will retire this year. Consider a random sample of 200 workers.

188) What is the probability that more than three of them will retire this year? Use the Poisson approximation to the binomial.

189) What is an estimate of the standard deviation of the number of people who will retire this year? Use the Poisson approximation to the binomial.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

From past experience, it is known 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year-olds is given this voice recognition test.

190) Find the probability at least 3 children do not recognize their mother's voice.

191) Find the probability all 20 children recognize their mother's voice.

192) Let the random variable X denote the number of children who do not recognize their mother's voice. Find the mean of X.

193) Let the random variable X denote the number of children who do not recognize their mother's voice. Find the variance of X.

194) Find the probability that at most 4 children do not recognize their mother's voice?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. A random sample of 25 customers is selected. Assume that customers' purchases are made independently, and let X represent the number of customers who purchase running shoes. (Hint: Solve using Excel.)

195) What is the probability that exactly 18 customers purchase running shoes?

196) What is the probability that no more than 19 customers purchase running shoes?

197) What is the probability that at least 17 customers purchase running shoes?

198) What is the probability that between 17 and 21 customers, inclusively, purchase running shoes?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

The number of people arriving at a bicycle repair shop follows a Poisson distribution with an average of 5 arrivals per hour. Let X represent the number of people arriving per hour.

199) What is the probability that seven people arrive at the bike repair shop in a one hour period of time?

200) What is the probability that at most seven people arrive at the bike repair shop in a one hour period of time?

201) What is the probability that more than seven people arrive at the bike repair shop in a one hour period of time?

202) What is the probability that between 4 and 9 people, inclusively, arrive at the bike repair shop in a one hour period of time?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

You have recently joined a country club. The number of times you expect to play golf in a month is represented by a random variable with a mean of 10 and a standard deviation of 2.2. Assume you pay monthly membership fees of $500 per month and pay an additional $50 per round of golf.

203) What is your average monthly bill from the country club?

A) $700

B) $800

C) $900

D) $1000

204) What is the standard deviation for your average monthly bill from the country club?

A) $220

B) $110

C) $324

D) $180

205) Which of the following is false regarding the normal distribution?

A) The mean, median, and mode are equal.

B) The frequency of values peaks at the mean, regardless of the value of the mean or variance.

C) 100% of the values fall between 3 standard deviations.

D) The shape of the distribution is symmetrical around the mean.

206) One normal distribution has a mean of 5 and a standard deviation of 2. A second normal distribution has a mean of 6 and a standard deviation of 1. Which of the following statements is true?

A) The width of the first distribution is wider than the second distribution.

B) The central location of the first distribution is higher than the second distribution.

C) The dispersions of both distributions are the same.

D) The locations of both distributions are the same.

207) Let the random variable Z follow a standard normal distribution. Find the value k, such

that P(Z > k) = 0.73.

A) 0.27

B) 0.73

C) -0.16

D) -0.61

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

Let the random variable X follow a normal distribution with a mean of 17.1 and a standard deviation of 3.2.

208) What is P(X > 16)?

A) 0.3401

B) 0.6331

C) 0.3669

D) 0.8326

209) What is P(15 < X < 20)?

A) 0.5581

B) 0.1814

C) 0.5640

D) 0.2546

210) The mean of a normally distributed group of weekly incomes for a group of executives is $2,400 and the standard deviation is $600. What is the z-score for an income of $1,500/week?

A) -1.5

B) -1.0

C) 2.5

D) 1.9

211) Let the random variable Z follow a standard normal distribution. Find the value k, such

that P(-0.62 < Z < k) = 0.43.

A) 0.20

B) 0.52

C) 0.12

D) 0.56

212) The normal probabilities are calculated using the table of standard normal distribution where the mean and standard deviations are, respectively:

A) 1 and 1.

B) 10 and 0.

C) 0 and 1.

D) 0 and 10.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

Let the random variable Z follow a standard normal distribution.

213) What is P(Z > 1.2)?

A) 0.1112

B) 0.8849

C) 0.1151

D) 0.6112

214) What is P(Z > -0.21)?

A) 0.4207

B) 0.4168

C) 0.5793

D) 0.5832

215) What is P(0.33 < Z < 0.45)?

A) 0.5443

B) 0.0443

C) 0.4557

D) 0.1515

216) The distribution of annual incomes of a sample of college graduates is normally distributed with a mean of $52,000 and a standard deviation of 1,000. About 68 percent of the incomes lie between what two income levels?

A) 52,000 and 62,000

B) 50,000 and 60,000

C) 51,000 and 53,000

D) 53,000 and 57,000