TRUE/FALSE.  Write 'T' if the statement is true and 'F' if the statement is false. 

1) 

Interviews, statistical sampling, and company reports provide input data for quantitative analysis models. 

1) 

_______ 

2) 

In the early 1900s, Henry Ford pioneered the principles of the scientific approach to management. 

2) 

_______ 

3) 

Managers do not need to be familiar with the limitations, assumptions, and/or specific applicability of the quantitative analysis technique to use it for accurate decision making. 

3) 

_______ 

4) 

During World War II, many new scientific and quantitative techniques were developed to assist the military, and these developments were so successful that many companies started using similar techniques in managerial decision making and planning after the war. 

4) 

_______ 

5) 

When a problem is difficult to quantify, it may be necessary to develop unspecific objectives. 

5) 

_______ 

6) 

The Quantitative Analysis Approach consists of six steps. 

6) 

_______ 

7) 

A mathematical model shows the relationship between quantifiable and non-quantifiable information. 

7) 

_______ 

8) 

Decision variables may also be called parameters. 

8) 

_______ 

9) 

Model variables can be controllable or uncontrollable. 

9) 

_______ 

10) 

A series of steps or procedures that are repeated is known as an algorithm. 

10) 

______ 

11) 

A model is a representation of a situation. 

11) 

______ 

12) 

A parameter is a measurable quantity that may vary or is subject to change. 

12) 

______ 

13) 

Trying various approaches and picking the one resulting in the best decision is called incomplete enumeration. 

13) 

______ 

14) 

All problems can be solved by considering only the quantitative issues. 

14) 

______ 

15) 

A profit equation is an example of a schematic model. 

15) 

______ 

16) 

Testing the data and model should be done before the results have been analyzed. 

16) 

______ 

17) 

Sensitivity analysis helps us estimate the effect of known and unknown errors in our model. 

17) 

______ 

18) 

Models can help us analyze a problem and sell a decision to those who must implement it. 

18) 

______ 

19) 

A sensitivity analysis allows a manager to answer the "what if" questions. 

19) 

______ 

20) 

One problem in using a quantitative model is that the necessary data may be unavailable. 

20) 

______ 

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

21) 

Which of the following terms is interchangeable with quantitative analysis? 

21) 

______ 

A) 

statistics 

B) 

economics 

C) 

management science 

D) 

financial analysis 

E) 

None of the above 

22) 

Operations Research is known as 

22) 

______ 

A) 

the science of numerical analysis. 

B) 

the science of modeling. 

C) 

the science of sensitivity analysis. 

D) 

the science of better. 

E) 

None of the above 

23) 

Who is credited with pioneering the principles of the scientific approach to management? 

23) 

______ 

A) 

Henri Fayol 

B) 

Charles Babbage 

C) 

Frederick W. Taylor 

D) 

John R. Locke 

E) 

Adam Smith 

24) 

A(n) ________ is a representation of reality or a real-life situation. 

24) 

______ 

A) 

algorithm 

B) 

objective 

C) 

model 

D) 

analysis 

E) 

None of the above 

25) 

A measurable quantity that may vary, or is subject to change, and can be controlled is known as a(n) 

25) 

______ 

A) 

algorithm. 

B) 

solution. 

C) 

decision variable. 

D) 

parameter. 

E) 

None of the above 

26) 

A set of logical and mathematical operations performed in a specific sequence is called a(n) 

26) 

______ 

A) 

complete enumeration. 

B) 

algorithm. 

C) 

objective. 

D) 

diagnostic analysis. 

E) 

None of the above 

27) 

The ability to examine the variability of a solution due to changes in the formulation of a problem is an important part of the analysis of the results. This type of analysis is called ________ analysis. 

27) 

______ 

A) 

implicit 

B) 

normal 

C) 

scale 

D) 

sensitivity 

E) 

objective 

28) 

Which of the following is not one of the steps in the quantitative analysis approach? 

28) 

______ 

A) 

Implementing the Results 

B) 

Observing a hypothesis 

C) 

Developing a Solution 

D) 

Testing a Solution 

E) 

Defining the Problem 

29) 

The condition of improper data yielding misleading results is referred to as 

29) 

______ 

A) 

break-even point. 

B) 

garbage in, garbage out. 

C) 

uncontrollable variable. 

D) 

postoptimality. 

E) 

None of the above 

30) 

Expressing profits through the relationship among unit price, fixed costs, and variable costs is an example of 

30) 

______ 

A) 

a postoptimality relationship. 

B) 

a quantitative analysis model. 

C) 

a sensitivity analysis model. 

D) 

a parameter specification model. 

E) 

None of the above 

31) 

The widespread applicability of operations research methods to business followed which war? 

31) 

______ 

A) 

The Korean War 

B) 

The Vietnam War 

C) 

The U.S. Civil War 

D) 

World War II 

E) 

World War I 

32) 

Which of the following statement(s) are true regarding the advantages of mathematical modeling? 

32) 

______ 

A) 

Models can save time. 

B) 

Models may be the only way to solve some large and complex problems in a timely manner. 

C) 

Models can help decision makers formulate problems. 

D) 

Models accurately represent reality. 

E) 

All of the above 

33) 

A measurable quantity that is inherent in the problem is called a(n) 

33) 

______ 

A) 

decision variable. 

B) 

enumeration variable. 

C) 

parameter. 

D) 

uncontrollable variable. 

E) 

algorithm. 

34) 

Trying various approaches and picking the one that results in the best decision is called 

34) 

______ 

A) 

the trial-and-error method. 

B) 

incomplete enumeration. 

C) 

algorithmic approximation. 

D) 

sensitivity analysis. 

E) 

complete enumeration. 

35) 

Models that do not involve risk or chance are 

35) 

______ 

A) 

postoptimality models. 

B) 

deterministic models. 

C) 

MIS models. 

D) 

probabilistic models. 

E) 

None of the above 

36) 

If input data are accurate to three significant digits, then the solution results can be accurate to how many significant digits? 

36) 

______ 

A) 

one 

B) 

six 

C) 

four 

D) 

two 

E) 

three 

37) 

Postoptimality analysis is most closely associated with 

37) 

______ 

A) 

developing a model. 

B) 

writing a computer program. 

C) 

collecting input data. 

D) 

sensitivity analysis. 

E) 

None of the above 

38) 

The break-even point is an example of a 

38) 

______ 

A) 

sensitivity analysis model. 

B) 

postoptimality model. 

C) 

quantitative analysis model. 

D) 

schematic model. 

E) 

None of the above 

39) 

Stochastic models are synonymous with 

39) 

______ 

A) 

qualitative models. 

B) 

deterministic models 

C) 

schematic models. 

D) 

conceptual models. 

E) 

None of the above 

40) 

A controllable variable is also called a 

40) 

______ 

A) 

measurable quantity. 

B) 

parameter. 

C) 

decision variable. 

D) 

mathematical model. 

E) 

None of the above 

41) 

Evaluating all possible values of a variable in a model is called 

41) 

______ 

A) 

variablization. 

B) 

complete enumeration. 

C) 

trial and error. 

D) 

an algorithm. 

E) 

None of the above 

42) 

What is the formula for the break-even point of a simple profit model? 

42) 

______ 

A) 

Fixed Cost / (Selling Price Per Unit —Variable Cost Per Unit) 

B) 

Selling Price Per Unit — (Fixed Cost / Variable Cost Per Unit) 

C) 

(Selling Price Per Unit —Variable Cost Per Unit) / Fixed Cost 

D) 

Fixed Cost / Variable Cost Per Unit 

E) 

Fixed Cost / (Variable Cost Per Unit — Selling Price Per Unit) 

43) 

The break-even point of a simple profit model represents a(n) 

43) 

______ 

A) 

uncontrollable variable. 

B) 

constant. 

C) 

decision variable. 

D) 

parameter. 

E) 

None of the above 

44) 

A(n) ________ model is one that is accurate and correctly represents the problem or system under investigation. 

44) 

______ 

A) 

robust 

B) 

valid 

C) 

optimal 

D) 

feasible 

E) 

sensitive 

45) 

Which Excel feature is an optimization technique that can maximize or minimize a quantity given a set of limitations or constraints? 

45) 

______ 

A) 

Analysis Tool-Pak 

B) 

Solver 

C) 

Goal Seek 

D) 

Algorithm Builder 

E) 

Optimizer 

46) 

Which Excel feature allows the user to specify a target or goal and the variable that is desired to change in order to achieve that goal? 

46) 

______ 

A) 

Goal Search 

B) 

Solver 

C) 

Target Search 

D) 

Goal Seek 

E) 

Target Seek 

47) 

All of the following are real computer applications that perform quantitative analysis except 

47) 

______ 

A) 

Goal Seek in Excel. 

B) 

Solver in Excel. 

C) 

QA for Windows. 

D) 

POM-QM for Windows. 

E) 

Excel QM. 

48) 

As one attempts to develop a model, which of the following problems might she encounter? 

48) 

______ 

A) 

The problem may not fit a textbook approach. 

B) 

Not everyone will understand the problem in the same way. 

C) 

There will be no data available to test the model. 

D) 

All of the above 

E) 

None of the above 

49) 

Which of the following is a picture, drawing, or chart of reality? 

49) 

______ 

A) 

abstract model 

B) 

physical model 

C) 

scale model 

D) 

mathematical model 

E) 

schematic model 

50) 

Which of the following is not considered a possible problem in the quantitative analysis approach? 

50) 

______ 

A) 

validity of the data 

B) 

subjective solutions 

C) 

lack of commitment 

D) 

hard-to-understand mathematics 

E) 

resistance to change 

ESSAY.  Write your answer in the space provided or on a separate sheet of paper. 

51) 

Quantitative analysis is ________. 

52) 

Identify the steps of the quantitative analysis approach. 

53) 

A controllable variable is also called a ________ variable. 

54) 

A picture, drawing, or chart of reality is a ________ model 

55) 

Identify some possible problems in the quantitative analysis approach. 

56) 

Identify three potential problems with people (two with management and one with the quantitative analysts themselves) that may hinder successful implementation of a quantitative model. 

57) 

In making a decision, both ________ and quantitative factors must be considered. 

58) 

Inaccurate model input data leads to inaccurate model solutions. This phenomenon is commonly referred to as ________. 

59) 

The solution process of ________ implies that we look at all possible solutions. 

60) 

Once we have a solution, we should then perform ________ analysis. 

61) 

________ models do not involve risk or chance. 

62) 

________ models are synonymous with stochastic models. 

63) 

How can an analyst overcome the threats to successful implementation of a quantitative model? 

TRUE/FALSE.  Write 'T' if the statement is true and 'F' if the statement is false. 

64) 

Subjective probability implies that we can measure the relative frequency of the values of the random variable. 

64) 

______ 

65) 

The use of "expert opinion" is one way to approximate subjective probability values. 

65) 

______ 

66) 

Mutually exclusive events exist if only one of the events can occur on any one trial. 

66) 

______ 

67) 

Stating that two events are statistically independent means that the probability of one event occurring is independent of the probability of the other event having occurred. 

67) 

______ 

68) 

Saying that a set of events is collectively exhaustive implies that one of the events must occur. 

68) 

______ 

69) 

Saying that a set of events is mutually exclusive and collectively exhaustive implies that one and only one of the events can occur on any trial. 

69) 

______ 

70) 

A posterior probability is a revised probability. 

70) 

______ 

71) 

Bayes' theorem enables us to calculate the probability that one event takes place knowing that a second event has or has not taken place. 

71) 

______ 

72) 

A probability density function is a mathematical way of describing Bayes' theorem. 

72) 

______ 

73) 

The probability, P, of any event or state of nature occurring is greater than or equal to 0 and less than or equal to 1. 

73) 

______ 

74) 

A probability is a numerical statement about the chance that an event will occur. 

74) 

______ 

75) 

If two events are mutually exclusive, the probability of both events occurring is simply the sum of the individual probabilities. 

75) 

______ 

76) 

Given two statistically dependent events (A,B), the conditional probability of P(A|B) = P(B)/P(AB). 

76) 

______ 

77) 

Given two statistically independent events (A,B), the joint probability of P(AB) = P(A) + P(B). 

77) 

______ 

78) 

Given three statistically independent events (A,B,C), the joint probability of P(ABC) = P(A) × P(B) × P(C). 

78) 

______ 

79) 

Given two statistically independent events (A,B), the conditional probability P(A|B) = P(A). 

79) 

______ 

80) 

Suppose that you enter a drawing by obtaining one of 20 tickets that have been distributed.  By using the classical method, you can determine that the probability of your winning the drawing is 0.05. 

80) 

______ 

81) 

Assume that you have a box containing five balls two red and three white.  You draw a ball two times, each time replacing the ball just drawn before drawing the next.  The probability of drawing only one white ball is 0.20. 

81) 

______ 

82) 

If we roll a single die twice, the probability that the sum of the dots showing on the two rolls equals four (4), is 1/6. 

82) 

______ 

83) 

For two events A and B that are not mutually exclusive, the probability that either A or B will occur is P(A) × P(B) - P(A and B). 

83) 

______ 

84) 

If we flip a coin three times, the probability of getting three heads is 0.125. 

84) 

______ 

85) 

Consider a standard 52-card deck of cards.  The probability of drawing either a seven or a black card is 7/13. 

85) 

______ 

86) 

If a bucket has three black balls and seven green balls, and we draw balls without replacement, the probability of drawing a green ball is independent of the number of balls previously drawn. 

86) 

______ 

87) 

Assume that you have an urn containing 10 balls of the following description
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)

If you draw a numbered ball (N), the probability that this ball is white (W) is 0.667. 

87) 

______ 

88) 

Assume that you have an urn containing 10 balls of the following description
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)

If you draw a numbered ball (N), the probability that this ball is white (W) is 0.60. 

88) 

______ 

89) 

Assume that you have an urn containing 10 balls of the following description
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)

If you draw a lettered ball (L), the probability that this ball is white (W) is 0.571. 

89) 

______ 

90) 

The joint probability of two or more independent events occurring is the sum of their marginal or simple probabilities. 

90) 

______ 

91) 

The number of bad checks written at a local store is an example of a discrete random variable. 

91) 

______ 

92) 

Given the following distribution

Outcome	Value of 
Random Variable	Probability	
A	1	 .4	
B	2	 .3	
C	3	 .2	
D	4	 .1	

The expected value is 3. 

92) 

______ 

93) 

A new young executive is perplexed at the number of interruptions that occur due to employee relations. She has decided to track the number of interruptions that occur during each hour of her day. Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day. The data is shown below.

Number of Interruptions in 1 hour	Probability	
0 interruption	 .5	
1 interruptions	 .3	
2 interruptions	 .1	
3 interruptions	 .1	
 
On average, she should expect 0.8 interruptions per hour. 

93) 

______ 

94) 

A new young executive is perplexed at the number of interruptions that occur due to employee relations. She has decided to track the number of interruptions that occur during each hour of her day. Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day. The data is shown below.

Number of Interruptions in 1 hour	Probability	
0 interruption	 .4	
1 interruptions	 .3	
2 interruptions	 .2	
3 interruptions	 .1	
 
On average, she should expect 1.0 interruptions per hour. 

94) 

______ 

95) 

The expected value of a binomial distribution is expressed as np, where n equals the number of trials and p equals the probability of success of any individual trial. 

95) 

______ 

96) 

The standard deviation equals the square of the variance. 

96) 

______ 

97) 

The probability of obtaining specific outcomes in a Bernoulli process is described by the binomial probability distribution. 

97) 

______ 

98) 

The variance of a binomial distribution is expressed as np/(1-p), where n equals the number of trials and p equals the probability of success of any individual trial. 

98) 

______ 

99) 

The F distribution is a continuous probability distribution that is helpful in testing hypotheses about variances. 

99) 

______ 

100) 

The mean and standard deviation of the Poisson distribution are equal. 

100) 

_____ 

101) 

In a normal distribution the Z value represents the number of standard deviations from a value X to the mean. 

101) 

_____ 

102) 

Assume you have a normal distribution representing the likelihood of completion times.  The mean of this distribution is 10, and the standard deviation is 3.  The probability of completing the project in 8 or fewer days is the same as the probability of completing the project in 18 days or more. 

102) 

_____ 

103) 

Assume you have a normal distribution representing the likelihood of completion times.  The mean of this distribution is 10, and the standard deviation is 3.  The probability of completing the project in 7 or fewer days is the same as the probability of completing the project in 13 days or more. 

103) 

_____ 

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

104) 

The classical method of determining probability is 

104) 

_____ 

A) 

objective probability. 

B) 

joint probability. 

C) 

conditional probability. 

D) 

subjective probability. 

E) 

marginal probability. 

105) 

Subjective probability assessments depend on 

105) 

_____ 

A) 

the total number of trials. 

B) 

the number of occurrences of the event. 

C) 

experience and judgment. 

D) 

the relative frequency of occurrence. 

E) 

None of the above 

106) 

If two events are mutually exclusive, then 

106) 

_____ 

A) 

they may also be collectively exhaustive. 

B) 

their probabilities can be added. 

C) 

the joint probability is equal to 0. 

D) 

if one occurs, the other cannot occur. 

E) 

All of the above 

107) 

A ________ is a numerical statement about the likelihood that an event will occur. 

107) 

_____ 

A) 

probability 

B) 

mutually exclusive construct 

C) 

standard deviation 

D) 

collectively exhaustive construct 

E) 

variance 

108) 

A conditional probability P(B|A) is equal to its marginal probability P(B) if 

108) 

_____ 

A) 

the events are mutually exclusive. 

B) 

P(A) = P(B). 

C) 

statistical dependence exists. 

D) 

it is a joint probability. 

E) 

statistical independence exists. 

109) 

The equation P(A|B) = P(AB)/P(B) is 

109) 

_____ 

A) 

only relevant when events A and B are collectively exhaustive. 

B) 

the marginal probability. 

C) 

the formula for a conditional probability. 

D) 

the formula for a joint probability. 

E) 

None of the above 

110) 

Suppose that we determine the probability of a warm winter based on the number of warm winters experienced over the past 10 years.  In this case, we have used ________. 

110) 

_____ 

A) 

the classical method 

B) 

subjective probability 

C) 

relative frequency 

D) 

the logical method 

E) 

None of the above 

111) 

Bayes' theorem is used to calculate 

111) 

_____ 

A) 

revised probabilities. 

B) 

joint probabilities. 

C) 

marginal probabilities. 

D) 

subjective probabilities. 

E) 

prior probabilities. 

112) 

If the sale of ice cream and pizza are independent, then as ice cream sales decrease by 60 percent during the winter months, pizza sales will 

112) 

_____ 

A) 

increase by 60 percent. 

B) 

decrease by 60 percent. 

C) 

increase by 40 percent. 

D) 

decrease by 40 percent. 

E) 

be unrelated. 

113) 

If P(A) = 0.3, P(B) = 0.2, P(A and B) = 0.0 , what can be said about events A and B? 

113) 

_____ 

A) 

They are posterior probabilities. 

B) 

They are independent. 

C) 

They are mutually exclusive. 

D) 

None of the above 

E) 

All of the above 

114) 

Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same.  What is the probability that one of the first three golfers that registered for the tournament will win? 

114) 

_____ 

A) 

0.700 

B) 

0.299 

C) 

0.001 

D) 

0.300 

E) 

0.100 

115) 

Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same.  Six of the entrants are female and two of those are older than 40 years old.  Three of the men are older than 40 years old.  What is the probability that the winner will be either female or older than 40 years old? 

115) 

_____ 

A) 

0.200 

B) 

0.000 

C) 

1.100 

D) 

0.198 

E) 

0.900 

116) 

Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same.  Six of the entrants are female and two of those are older than 40 years old.  Three of the men are older than 40 years old.  What is the probability that the winner will be a female who is older than 40 years old? 

116) 

_____ 

A) 

0.900 

B) 

1.100 

C) 

0.000 

D) 

0.200 

E) 

0.198 

117) 

"The probability of event B, given that event A has occurred" is known as a ________ probability. 

117) 

_____ 

A) 

marginal 

B) 

conditional 

C) 

simple 

D) 

joint 

E) 

continuous 

118) 

When does P(A|B) = P(A)? 

118) 

_____ 

A) 

when A and B are mutually exclusive 

B) 

when A and B are statistically independent 

C) 

when P(B) = 0 

D) 

when A and B are statistically dependent 

E) 

when A and B are collectively exhaustive 

119) 

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to "win" the tickets. There are 6 secretaries, 5 consultants and 4 partners in the firm. Which of the following statements is not true? 

119) 

_____ 

A) 

The probability of a consultant winning a ticket on the first draw is 1/3. 

B) 

The probability of a secretary winning a ticket on the first draw is 6/15. 

C) 

The probability of a partner winning a ticket on the second draw given that a secretary won a ticket on the first draw is 4/14. 

D) 

The probability of two secretaries winning both tickets is 1/7. 

E) 

The probability of a secretary winning a ticket on the second draw given that a consultant won a ticket on the first draw is 6/15. 

120) 

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to "win" the tickets. There are 6 secretaries, 5 consultants, and 4 partners in the firm. Which of the following statements is true? 

120) 

_____ 

A) 

The probability of a partner winning on the second draw given that a partner won on the first draw is 3/14. 

B) 

The probability of a consultant winning on the second draw given that a consultant won on the first draw is 5/14. 

C) 

The probability of a partner winning on the second draw given that a secretary won on the first draw is 8/30. 

D) 

The probability of a secretary winning on the second draw given that a secretary won on the first draw is 2/15. 

E) 

None of the above are true. 

121) 

A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to "win" the tickets. There are 6 secretaries, 5 consultants, and 4 partners in the firm. Which of the following statements is true? 

121) 

_____ 

A) 

The probability of a secretary winning on the second draw given that a consultant won on the first draw is the same as the probability of a consultant winning on the second draw given that a secretary won on the first draw. 

B) 

The probability that both tickets will be won by partners is the same as the probability that a consultant and secretary will win. 

C) 

The probability of a secretary and a consultant winning is the same as the probability of a secretary and secretary winning. 

D) 

The probability of two secretaries winning is the same as the probability of a secretary winning on the second draw given that a consultant won on the first draw. 

E) 

None of the above are true. 

122) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200 students, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random, what is the probability that the student is either enrolled in accounting or statistics, but not both? 

122) 

_____ 

A) 

0.05 

B) 

0.50 

C) 

0.45 

D) 

0.40 

E) 

None of the above 

123) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200 students, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random, what is the probability that the student is enrolled in accounting? 

123) 

_____ 

A) 

0.25 

B) 

0.50 

C) 

0.30 

D) 

0.20 

E) 

None of the above 

124) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200 students, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random, what is the probability that the student is enrolled in statistics? 

124) 

_____ 

A) 

0.05 

B) 

0.25 

C) 

0.20 

D) 

0.30 

E) 

None of the above 

125) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200 students, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random, what is the probability that the student is enrolled in both statistics and accounting? 

125) 

_____ 

A) 

0.20 

B) 

0.06 

C) 

0.25 

D) 

0.05 

E) 

None of the above 

126) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200 students, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random and found to be enrolled in statistics, what is the probability that the student is also enrolled in accounting? 

126) 

_____ 

A) 

0.25 

B) 

0.05 

C) 

0.20 

D) 

0.30 

E) 

None of the above 

127) 

Suppose that when the temperature is between 35 and 50 degrees, it has historically rained 40% of the time.  Also, historically, the month of April has had a temperature between 35 and 50 degrees on 25 days.  You have scheduled a golf tournament for April 12.  What is the probability that players will experience rain and a temperature between 35 and 50 degrees? 

127) 

_____ 

A) 

1.000 

B) 

0.833 

C) 

0.400 

D) 

0.333 

E) 

0.480 

128) 

Suppose that, historically, April has experienced rain and a temperature between 35 and 50 degrees on 20 days.  Also, historically, the month of April has had a temperature between 35 and 50 degrees on 25 days.  You have scheduled a golf tournament for April 12.  If the temperature is between 35 and 50 degrees on that day, what will be the probability that the players will get wet? 

128) 

_____ 

A) 

0.667 

B) 

0.556 

C) 

1.000 

D) 

0.333 

E) 

0.800 

129) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random, what is the probability that the student is enrolled in neither accounting nor statistics? 

129) 

_____ 

A) 

0.45 

B) 

0.50 

C) 

0.05 

D) 

0.55 

E) 

None of the above 

130) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random, what is the probability that the student is not enrolled in accounting? 

130) 

_____ 

A) 

0.50 

B) 

0.25 

C) 

0.20 

D) 

0.30 

E) 

None of the above 

131) 

At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course.  Of these 200, 50 are also enrolled in an introductory accounting course.  There are an additional 250 business students enrolled in accounting but not enrolled in statistics.  If a business student is selected at random, what is the probability that the student is not enrolled in statistics? 

131) 

_____ 

A) 

0.20 

B) 

0.25 

C) 

0.80 

D) 

0.05 

E) 

None of the above 

132) 

A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are randomly selected as they come off the production line, what is the probability that the second item will be defective? 

132) 

_____ 

A) 

0.005 

B) 

0.18 

C) 

0.05 

D) 

0.20 

E) 

None of the above 

133) 

A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are randomly selected as they come off the production line, what is the probability that both are defective (assuming that they are independent)? 

133) 

_____ 

A) 

0.1000 

B) 

0.0250 

C) 

0.2000 

D) 

0.0100 

E) 

0.0025 

134) 

A company is considering producing some new Gameboy electronic games.  Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities.  In the past, the successful products were predicted to be successful based on market research 90 percent of the time.  However, for products that failed, the market research predicted these would be successes 20 percent of the time.  If market research is performed for a new product, what is the probability that the results indicate a successful market for the product and the product is actually not successful? 

134) 

_____ 

A) 

0.63 

B) 

0.06 

C) 

0.27 

D) 

0.24 

E) 

0.07 

135) 

A company is considering producing some new Gameboy electronic games.  Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities.  In the past, the successful products were predicted to be successful based on market research 90 percent of the time.  However, for products that failed, the market research predicted these would be successes 20 percent of the time.  If market research is performed for a new product, what is the probability that the results indicate an unsuccessful market for the product and the product is actually successful? 

135) 

_____ 

A) 

0.07 

B) 

0.24 

C) 

0.06 

D) 

0.21 

E) 

0.63 

136) 

A company is considering producing some new Gameboy electronic games.  Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities.  In the past, the successful products were predicted to be successful based on market research 90 percent of the time.  However, for products that failed, the market research predicted these would be successes 20 percent of the time.  If market research is performed for a new product, what is the probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful? 

136) 

_____ 

A) 

0.21 

B) 

0.06 

C) 

0.63 

D) 

0.07 

E) 

0.24 

137) 

A company is considering producing some new Gameboy electronic games.  Based on past records, management believes that there is a 70 percent chance that each of these will be successful, and a 30 percent chance of failure. Market research may be used to revise these probabilities.  In the past, the successful products were predicted to be successful based on market research 90 percent of the time.  However, for products that failed, the market research predicted these would be successes 20 percent of the time.  If market research is performed for a new product, what is the probability that the product will be successful if the market research indicates a success? 

137) 

_____ 

A) 

0.90 

B) 

0.10 

C) 

0.91 

D) 

0.09 

E) 

0.63 

138) 

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge. Management believes 60 percent of customers will take advantage of this service. They are also considering offering customers the option of opening an account and receiving monthly bills. They believe 60 percent of their customers (regardless of whether or not they use the pick-up service) will use the account service. If the two services are introduced to the market, what is the probability a customer uses both services? 

138) 

_____ 

A) 

0.60 

B) 

0.12 

C) 

0.36 

D) 

0.24 

E) 

None of the above 

139) 

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge. Management believes 60 percent of the existing customers will take advantage of this service. They are also considering offering customers the option of opening an account and receiving monthly bills. They believe 60 percent of customers (regardless of whether or not they use the pick-up service) will use the account service. If the two services are introduced to the market, what is the probability that a customer uses only one of these services? 

139) 

_____ 

A) 

0.48 

B) 

0.40 

C) 

0.60 

D) 

0.24 

E) 

None of the above 

140) 

A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge. Management believes 60 percent of the existing customers will take advantage of this service. They are also considering offering customers the option of opening an account and receiving monthly bills. They believe 60 percent of customers (regardless of whether or not they use the pick-up service) will use the account service. If the two services are introduced to the market, what is the probability a customer uses neither of these services? 

140) 

_____ 

A) 

0.24 

B) 

0.80 

C) 

0.16 

D) 

0.36 

E) 

None of the above 

141) 

A company is considering producing some new Gameboy electronic games.  Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities.  In the past, the successful products were predicted to be successful based on market research 90 percent of the time.  However, for products that failed, the market research predicted these would be successes 20 percent of the time.  If market research is performed for a new product, what is the probability that the product will be successful if the market research indicates a failure? 

141) 

_____ 

A) 

0.90 

B) 

0.91 

C) 

0.63 

D) 

0.20 

E) 

0.23 

142) 

Which distribution is helpful in testing hypotheses about variances? 

142) 

_____ 

A) 

normal distribution 

B) 

F distribution 

C) 

exponential distribution 

D) 

Poisson distribution 

E) 

binomial distribution 

143) 

A company is considering producing two new electronic games designed for the popular Gameboy toy.  Based on market data, management believes there is a 60 percent chance that a "cops and robbers" game will be successful and a 40 percent chance that a "let's play house" game will be successful.  As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other.  If two products are introduced to the market, what is the probability that both are successful? 

143) 

_____ 

A) 

0.60 

B) 

0.36 

C) 

0.24 

D) 

0.12 

E) 

None of the above 

144) 

A company is considering producing two new electronic games designed for the popular Gameboy toy.  Based on market data, management believes that there is a 60 percent chance that a "cops and robbers" game will be successful and a 40 percent chance that "let's play house" game will be successful.  As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other.  If two products are introduced to the market, what is the probability that both are failures? 

144) 

_____ 

A) 

0.16 

B) 

0.80 

C) 

0.36 

D) 

0.24 

E) 

None of the above 

145) 

A company is considering producing some new Gameboy electronic games.  Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities.  In the past, the successful products were predicted to be successful based on market research 90 percent of the time.  However, for products that failed, the market research predicted these would be successes 20 percent of the time.  If market research is performed for a new product, what is the probability that the results indicate a successful market for the product and the product actually is successful? 

145) 

_____ 

A) 

0.60 

B) 

0.63 

C) 

0.54 

D) 

0.90 

E) 

None of the above 

146) 

The expected value of a probability distribution is 

146) 

_____ 

A) 

the measure of the spread of the distribution. 

B) 

the probability density function. 

C) 

the variance of the distribution. 

D) 

the range of continuous values from point A to point B, inclusive. 

E) 

the average value of the distribution. 

147) 

Which of the following is not true for discrete random variables? 

147) 

_____ 

A) 

A binomial random variable is considered discrete. 

B) 

The expected value is the weighted average of the values. 

C) 

They can assume only a countable number of values. 

D) 

The probability of each value of the random variable must be 0. 

E) 

The probability values always sum up to 1. 

148) 

The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, or 2. The probabilities are the same for each of these (1/3).  If X is the number of calls arriving in a five-minute time period, what is the mean of X? 

148) 

_____ 

A) 

4/3 

B) 

1 

C) 

2/3 

D) 

1/3 

E) 

None of the above 

149) 

The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, 2, 3, 4, 5, or 6. The probabilities are the same for each of these (1/7).  If X is the number of calls arriving in a five-minute time period, what is the mean of X? 

149) 

_____ 

A) 

4 

B) 

3 

C) 

5 

D) 

2 

E) 

None of the above 

150) 

A discrete random variable has a mean of 400 and a variance of 64.  What is the standard deviation? 

150) 

_____ 

A) 

8 

B) 

400 

C) 

64 

D) 

20 

E) 

None of the above 

151) 

Which of the following is not true about continuous random variables? 

151) 

_____ 

A) 

The area under each of the curves represents probabilities. 

B) 

The entire area under each of the curves equals 1. 

C) 

Some may be described by uniform distributions or exponential distributions. 

D) 

They have an infinite set of values. 

E) 

They can only be integer values. 

152) 

Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that exactly 2 customers would be willing to switch their cable? 

152) 

_____ 

A) 

0.1 

B) 

0.137 

C) 

0.04 

D) 

0.794 

E) 

0.206 

153) 

Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that no more than 3 customers would be willing to switch their cable? 

153) 

_____ 

A) 

0.589 

B) 

0.85 

C) 

0.20 

D) 

0.411 

E) 

0.15 

154) 

Properties of the normal distribution include 

154) 

_____ 

A) 

a continuous bell-shaped distribution. 

B) 

a discrete probability distribution. 

C) 

the number of trials is known and is either 1, 2, 3, 4, 5, etc. 

D) 

use in queuing. 

E) 

the random variable can assume only a finite or limited set of values. 

155) 

Which of the following characteristics is true for a normal probability distribution? 

155) 

_____ 

A) 

It is symmetrical. 

B) 

The midpoint is also the mean. 

C) 

Sixty-eight percent of the area under the curve lies within one standard deviation of the mean. 

D) 

The area under the curve is 1. 

E) 

All of the above are true. 

156) 

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.  What is the probability that a student uses fewer than 600 minutes? 

156) 

_____ 

A) 

0.977 

B) 

0.023 

C) 

0.841 

D) 

0 

E) 

None of the above 

157) 

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.  What is the probability that a student uses fewer than 400 minutes? 

157) 

_____ 

A) 

0.023 

B) 

0.977 

C) 

0.159 

D) 

0 

E) 

None of the above 

158) 

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.  What is the probability that a student uses more than 350 minutes? 

158) 

_____ 

A) 

0.999 

B) 

0.001 

C) 

0.382 

D) 

0.618 

E) 

None of the above 

159) 

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.  What is the probability that a student uses more than 580 minutes? 

159) 

_____ 

A) 

0.0548 

B) 

0.848 

C) 

0.152 

D) 

0.903 

E) 

None of the above 

160) 

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).  What is the probability that the average price per square foot for a home is greater than $110? 

160) 

_____ 

A) 

0.977 

B) 

0 

C) 

0.023 

D) 

0.841 

E) 

None of the above 

161) 

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).  What is the probability that the average price per square foot for a home is greater than $90? 

161) 

_____ 

A) 

0.023 

B) 

0.159 

C) 

0 

D) 

0.977 

E) 

None of the above 

162) 

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).  What is the probability that the average price per square foot for a home is less than $85? 

162) 

_____ 

A) 

0.999 

B) 

0.382 

C) 

0.001 

D) 

0.618 

E) 

None of the above 

163) 

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).  What is the probability that the average price per square foot for a home is less than $108? 

163) 

_____ 

A) 

0.097 

B) 

0.152 

C) 

0.848 

D) 

0.945 

E) 

None of the above 

164) 

The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks.  The construction company must pay a penalty if the project is not finished by the due date in the contract.  If a construction company bidding on this contract puts in a due date of 80 weeks, what is the probability that they will have to pay a penalty? 

164) 

_____ 

A) 

1/8 

B) 

1.000 

C) 

0 

D) 

0.500 

E) 

None of the above 

165) 

The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks.  The construction company must pay a penalty if the project is not finished by the due date in the contract.  If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date, what due date (project week #) should be negotiated? 

165) 

_____ 

A) 

.81954 

B) 

92.8 

C) 

81.28 

D) 

81.82 

E) 

None of the above 

166) 

The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.  What is the probability that it will take less than 40 minutes? 

166) 

_____ 

A) 

0.50 

B) 

0.20 

C) 

1.00 

D) 

0.80 

E) 

None of the above 

167) 

The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.  What is the probability that it will take less than 35 minutes? 

167) 

_____ 

A) 

0.53983 

B) 

0.84134 

C) 

0.15866 

D) 

0.46017 

E) 

None of the above 

168) 

The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.  What is the probability that it will take more than 40 minutes? 

168) 

_____ 

A) 

0.5000 

B) 

0.0625 

C) 

0.2500 

D) 

1.000 

E) 

None of the above 

169) 

Queuing Theory makes use of the 

169) 

_____ 

A) 

uniform probability distribution. 

B) 

Poisson probability distribution. 

C) 

binomial probability distribution. 

D) 

normal probability distribution. 

E) 

None of the above 

170) 

The number of cars passing through an intersection in the next five minutes can usually be described by the 

170) 

_____ 

A) 

exponential distribution. 

B) 

uniform distribution. 

C) 

normal distribution. 

D) 

Poisson distribution. 

E) 

None of the above 

171) 

Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour.  What is the probability that in the next hour there will be exactly 12 arrivals? 

171) 

_____ 

A) 

0.1322 

B) 

0.0000 

C) 

0.7500 

D) 

0.0661 

E) 

None of the above 

172) 

Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour.  What is the probability that in the next hour there will be exactly 8 arrivals? 

172) 

_____ 

A) 

1.000 

B) 

0.175 

C) 

0.825 

D) 

0.200 

E) 

None of the above 

173) 

Which of the following statements concerning the F distribution is true? 

173) 

_____ 

A) 

The F distribution is useful in modeling customer arrivals. 

B) 

The F distribution is discrete. 

C) 

The F distribution is interchangeable with the normal distribution for large sample sizes. 

D) 

The F distribution is symmetrical. 

E) 

The F distribution is useful in testing hypotheses about variance. 

174) 

What is the F value associated with α = 0.05, numerator degrees of freedom (df1) equal to 4, and denominator degrees of freedom (df2) equal to 9? 

174) 

_____ 

A) 

3.63 

B) 

0.11 

C) 

0.18 

D) 

1.80 

E) 

6.0 

175) 

Which of the following characteristics is not true for the exponential distribution? 

175) 

_____ 

A) 

It is discrete probability distribution. 

B) 

It is also called the negative exponential distribution. 

C) 

It is used in dealing with queuing problems. 

D) 

The variance is the square of the expected value. 

E) 

It is used to describe the times between customer arrivals. 

176) 

The length of time that it takes the tollbooth attendant to service each driver can typically be described by the 

176) 

_____ 

A) 

exponential distribution. 

B) 

uniform distribution. 

C) 

normal distribution. 

D) 

Poisson distribution. 

E) 

None of the above 

177) 

The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3 per minute) when it comes to license renewals. The service time follows an exponential distribution. What is the probability that it will take less than 2 minutes for a particular customer to get a license renewal? 

177) 

_____ 

A) 

0.487 

B) 

0 

C) 

0.1 

D) 

0.513 

E) 

1 

178) 

The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3 per minute) when it comes to license renewals. The service time follows an exponential distribution. What is the probability that it will take less than 3 minutes for a particular customer to get a license renewal? 

178) 

_____ 

A) 

0.5 

B) 

0 

C) 

0.632 

D) 

1 

E) 

0.368 

179) 

Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that takes less than 1/2 of a minute between consecutive drivers? 

179) 

_____ 

A) 

0.167 

B) 

0.777 

C) 

0.5 

D) 

0.223 

E) 

1 

180) 

Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that takes more than 1/3 of a minute between consecutive drivers? 

180) 

_____ 

A) 

0.632 

B) 

0.632 

C) 

0.368 

D) 

0.111 

E) 

Not enough information given 

ESSAY.  Write your answer in the space provided or on a separate sheet of paper. 

181) 

An urn contains 7 blue and 3 yellow chips.  If the drawing of chips is done with replacement, determine the probability of
(a)	drawing three yellow chips.
(b)	drawing a blue chip on the first draw and a yellow chip on the second draw.
(c)	drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw.
(d)	drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw.
(e)	drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw. 

182) 

A market research study is being conducted to determine if a product modification will be well received by the public.  A total of 1,000 consumers are questioned regarding this product.
The table below provides information regarding this sample.

	Positive
Reaction	Neutral
Reaction	Negative
Reaction	
Male	240	60	100	
Female	260	220	120	

(a)	What is the probability that a randomly selected male would find this change unfavorable (negative)?
(b)	What is the probability that a randomly selected person would be a female who had a positive reaction?
(c)	If it is known that a person had a negative reaction to the study, what is the probability that the person is male? 

183) 

In a production run of 300 units, there are exactly 20 defective items and 280 good items.
(a)	What is the probability that a randomly selected item is defective?
(b)	If two items are sampled without replacement, what is the probability that both are good?
(c)	If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective? 

184) 

A new television program was viewed by 200 people (120 females and 80 males).  Of the females, 60 liked the program and 60 did not.  Of the males, 60 of the 80 liked the program.
(a)	What is the probability that a randomly selected individual liked the program?
(b)	If a male in this group is selected, what is the probability that he liked the program?
(c)	What is the probability that a randomly selected individual is a female and liked the program? 

185) 

Colonel Motors (an automobile company) has prepared a marketing campaign for its best selling car.  The focus of the campaign is quality, and it is claimed that 97 percent of the purchasers of this car have no complaints in the first year.  You and your sister Kim have each purchased one of these cars.
(a)	What is the probability that neither of you has a complaint about the car in the first year if the advertising claim is true?
(b)	What is the probability that exactly one of you has a complaint about the car in the first year if the advertising claim is true? 

186) 

A local "home TV repair service" company has two repairmen who make all of the home repairs.  The company sends Repairman D on 70 percent of all jobs, because the likelihood of a "second follow-up call" within a week is only 0.08 compared to 0.20 for Repairman K.  If you had a recent repair job that is going to require a second follow-up call, what is the probability that Repairman K did your initial repair work? 

187) 

Our department store is having a sale on personal computers, of which three are in stock (no rain checks).  There is a certain probability of selling none.  The probability of selling one is twice as great as the probability of selling none.  The probability of selling two is three times the probability of selling none.  Finally, the probability of selling all the personal computers is four times as great as the probability of selling none.  In a table, list the outcomes and their probabilities.  Hint Let the probability of selling none equal x. 

188) 

ABC Manufacturing has 6 machines that perform a particular task.  Breakdowns occur frequently for this machine.  Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution

Number of Breakdowns	Probability	
0	0.4	
1	0.3	
2	0.2	
3	0.1	
More than 3	0.0	
 
(a) What is the expected number of breakdowns in any given day?
(b) What is the variance for this distribution?
(c) What is the probability that there will be at least 2 breakdowns in a day? 

189) 

Fast Service Store has maintained daily sales records on the various size "Cool Drink" sales. 

"Cool Drink" Price	Number Sold	
$0.50	75	
$0.75	120	
$1.00	125	
$1.25	80	
Total	400	
 
Assuming that past performance is a good indicator of future sales,
(a)	what is the probability of a customer purchasing a $1.00 "Cool Drink?"
(b)	what is the probability of a customer purchasing a $1.25 "Cool Drink?"
(c)	what is the probability of a customer purchasing a "Cool Drink" that costs greater than or equal to $1.00?
(d)	what is the expected value of a "Cool Drink"?
(e)	what is the variance of a "Cool Drink"? 

190) 

In a given office, the color printer breaks down with a probability of 20% in any month.  A binomial process is assumed for a period of 10 months.
(a) What is the probability that the printer breaks down exactly 2 times?
(b) What is the probability that the printer breaks down at most 1 time?
(c) What is the probability that the printer breaks down more than once? 

191) 

A southwestern tourist city has records indicating that the average daily temperature in the summer is 82 degrees F, which is normally distributed with a standard deviation of 3 degrees F.  Based on these records, determine
(a) the probability of a daily temperature between 79 degrees F and 85 degrees F.
(b) the probability that the daily temperature exceeds 90 degrees F.
(c) the probability that the daily temperature is below 76 degrees F. 

192) 

Using the table for finding the areas under normal curves, find the area under a normal curve with a mean of 200 and a standard deviation of 10 between the values of
(a) 200 to 205.
(b) 195 to 205.
(c) 200 to 215.
(d) 195 to 215.
(e) 186.5 to 217. 

193) 

The time required to complete a project is known to be normally distributed with a mean of 44 weeks and a standard deviation of 8 weeks.
(a) What is the probability that the project is finished in 40 weeks or fewer?
(b) What is the probability that the project is finished in 52 weeks or fewer?
(c) There is an 95 percent chance that the project will be finished in fewer than how many weeks? 

194) 

Compute the F value based on the following
(a) df1 = 2, df2 = 4, α = 0.01
(b) df1 = 3  df2 = 6, α = 0.05 

195) 

A call center receives calls from customers at a rate of 2 per min. The time between customer calls follows an exponential distribution.
(a)	What is the probability that it takes 1/3 of a minute or less between consecutive customer calls?
(b) What is the probability that it take 1/2 of a minute or more between consecutive customer calls? 

196) 

Arrivals in a university advising office during the week of registration are known to follow a Poisson distribution with an average of 4 people arriving each hour.
(a) What is the probability that exactly 4 people will arrive in the next hour?
(b) What is the probability that exactly 5 people will arrive in the next hour? 

197) 

Explain why event probabilities range from 0 to 1. 

198) 

Using a standard deck of 52 cards, explain why the situation of drawing a 7 and a club is not collectively exhaustive. 

199) 

Name five common probability distributions. 

200) 

If two events (A,B) are mutually exclusive, what is the probability of event A or event B occurring? 

201) 

If two events (A,B) are not mutually exclusive, what is the probability of event A or event B occurring? 

202) 

If two events (A,B) are independent, what is their joint probability? 

203) 

If two events (A,B) are dependent, what is the conditional probability of P(A|B)? 

204) 

If two events (A,B) are independent, then the conditional probability of P(A|B) = ________. 

205) 

Explain what a discrete random variable is. 

206) 

The exponential distribution often describes ________. 

207) 

List the two parameters of the normal distribution. 

208) 

In what way is the F distribution often used? 

209) 

List the parameter(s) of the Poisson distribution. 

 

1) 

TRUE 

2) 

FALSE 

3) 

FALSE 

4) 

TRUE 

5) 

FALSE 

6) 

FALSE 

7) 

FALSE 

8) 

FALSE 

9) 

TRUE 

10) 

TRUE 

11) 

TRUE 

12) 

FALSE 

13) 

FALSE 

14) 

FALSE 

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FALSE 

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TRUE 

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TRUE 

18) 

TRUE 

19) 

TRUE 

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TRUE 

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C 

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D 

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C 

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C 

25) 

C 

26) 

B 

27) 

D 

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B 

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B 

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B 

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D 

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E 

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C 

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A 

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B 

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E 

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D 

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C 

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E 

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C 

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B 

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A 

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C 

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B 

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B 

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D 

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C 

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D 

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E 

50) 

B 

51) 

the scientific approach to managerial decision making 

52) 

(1) Defining the Problem, (2) Developing a Model, (3) Acquiring Input Data, (4) Developing a Solution, (5) Testing the Solution, (6) Analyzing the Results, and (7) Implementing the Results 

53) 

decision 

54) 

schematic 

55) 

Answers will vary but may include conflicting viewpoints, ignoring the impact on other departments, poor assumptions, outdated solutions, difficulty matching the textbook approach, trading off model complexity with ease of understanding, poor input data, hard-to-understand mathematics, and having only one answer is limiting. 

56) 

Answers will vary but may include (1) lack of commitment by management, (2) resistance to change by management, and (3) lack of commitment by quantitative analysts. 

57) 

qualitative 

58) 

garbage in, garbage out 

59) 

complete enumeration 

60) 

sensitivity or postoptimality 

61) 

Deterministic 

62) 

Probabilistic 

63) 

Answers will vary; one solution is for analysts to work with users and take their feelings into account instead of telling them what to do. 

64) 

FALSE 

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TRUE 

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TRUE 

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TRUE 

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TRUE 

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TRUE 

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TRUE 

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TRUE 

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FALSE 

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TRUE 

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TRUE 

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TRUE 

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FALSE 

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FALSE 

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TRUE 

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TRUE 

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TRUE 

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FALSE 

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FALSE 

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FALSE 

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TRUE 

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TRUE 

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FALSE 

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TRUE 

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FALSE 

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TRUE 

90) 

FALSE 

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TRUE 

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FALSE 

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TRUE 

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TRUE 

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TRUE 

96) 

FALSE 

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TRUE 

98) 

FALSE 

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TRUE 

100) 

FALSE 

101) 

TRUE 

102) 

FALSE 

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TRUE 

104) 

A 

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C 

106) 

E 

107) 

A 

108) 

E 

109) 

C 

110) 

C 

111) 

A 

112) 

E 

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C 

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D 

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E 

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D 

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B 

118) 

B 

119) 

E 

120) 

A 

121) 

E 

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D 

123) 

C 

124) 

C 

125) 

D 

126) 

A 

127) 

D 

128) 

E 

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D 

130) 

E 

131) 

C 

132) 

C 

133) 

E 

134) 

B 

135) 

A 

136) 

E 

137) 

C 

138) 

C 

139) 

A 

140) 

C 

141) 

E 

142) 

B 

143) 

C 

144) 

D 

145) 

B 

146) 

E 

147) 

D 

148) 

B 

149) 

B 

150) 

A 

151) 

E 

152) 

B 

153) 

D 

154) 

A 

155) 

E 

156) 

A 

157) 

A 

158) 

A 

159) 

A 

160) 

C 

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D 

162) 

C 

163) 

D 

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D 

165) 

B 

166) 

A 

167) 

C 

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A 

169) 

B 

170) 

D 

171) 

D 

172) 

E 

173) 

E 

174) 

A 

175) 

A 

176) 

A 

177) 

A 

178) 

C 

179) 

B 

180) 

C 

181) 

(a) 0.027 (b) 0.210 (c) 0.700 (d) 0.300 (e) 0.300 

182) 

(a) 100/400 = 0.25  (b) 260/1000 = 0.260  (c) 100/220 = 0.4545 

183) 

(a) 20/300 = 0.067  (b) (280/300)(279/299) = 0.871  (c) (280/300)(20/299) = 0.062 

184) 

(a) 120/200 = 0.60  (b) 60/80 = 0.75  (c) 60/200 = 0.30 

185) 

(a) 0.97(0.97) = 0.9409  (b) 0.03(0.97) + 0.97(0.03) = 0.0582 

186) 

P(K|2nd) = 0.06/(.06+.056) = 0.517 

187) 

Outcome	Probability	
Sell 0	0.1	
Sell 1	0.2	
Sell 2	0.3	
Sell 3	0.4	

188) 

(a) expected value = 1.0 (b) variance = 1(.4) + 0(.3) + 1(.2) + 4(.1) = 1.0 (c) P(2 or more) = 0.2 + 0.1 = 0.3 

189) 

(a) 125/400 = 0.3125  (b) 80/400 = 0.20  (c) 205/400 = 0.5125  
(d) .5(.1875) + .75(.3) + 1(.3125) + 1.25(.2) = .88125  (e) 0.064 

190) 

(a) P(r=2) = 0.3020 (b) P(r≤1) = 0.3758 (c) P(r>1) = 0.6242 

191) 

(a) P(79<X<85) = 0.68268  (b) P(X>90) = 0.00383  (c) P(X<76) = 0.02275 

192) 

(a) 0.19146  (b) 0.38293  (c) 0.43319  (d) 0.62466  (e) 0.86693 

193) 

(a) 0.30854  (b) 0.84135  (c) 44 + 1.645(8) = 57.16 

194) 

(a) 18  (b) 4.76 

195) 

(a) 0.487 (b) 0.368 

196) 

(a) P(X=4) = 0.1954 (b) P(X=5) = 0.1563 

197) 

The number 0 represents no chance of occurrence, while 1 represents a 100 percent chance of occurrence.  Any number between 0 and 1 represents that particular event's chance of occurrence.  Any negative number or number exceeding 1 has no meaning for an event probability. 

198) 

It is possible to draw other cards that are non-clubs and also not a 7. 

199) 

Answers could vary, but may include binomial, normal, F, exponential, and Poisson. 

200) 

P(A or B) = P(A) + P(B) 

201) 

P(A or B) = P(A) + P(B) - P(A and B) 

202) 

P(AB) = P(A) × P(B) 

203) 

P(A|B) = P(AB)|P(B) 

204) 

P(A) 

205) 

A discrete random variable has a probability value assigned to each event.  These values must be between 0 and 1, and they must sum to 1. 

206) 

the time required to service a customer 

207) 

mean (μ) and standard deviation (σ) 

208) 

It is helpful in testing hypotheses about variances. 

209) 

the mean and the variance λ