Chapter 2

Quantitative Analysis for Management, 11e (Render)
Chapter 2 Probability Concepts and Applications

1) Subjective
implies that we can measure the relative frequency of the values of the random variable.
Answer: FALSE
Diff: 2
Topic: FUNDAMENTAL CONCEPTS
2) The use of "expert opinion" is one way to approximate subjective probability values.
Answer: TRUE
Diff: 1
3) Mutually exclusive events exist if only one of the events can occur on any one trial.
Answer: TRUE
Diff: 2
Topic: MUTUALLY EXCLUSIVE AND COLLECTIVELY EXHAUSTIVE EVENTS
4) 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.
Answer: TRUE
Diff: 2
Topic: STATISTICALLY INDEPENDENT EVENTS
5) Saying that a set of events is collectively exhaustive implies that one of the events must occur.
Answer: TRUE
Diff: 2
6) 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.
Answer: TRUE
Diff: 2
7) A posterior probability is a revised probability.
Answer: TRUE
Diff: 2
Topic: REVISING PROBABILITIES WITH BAYES' THEOREM
8) Bayes' theorem enables us to calculate the probability that one event takes place knowing that a second event
has or has not taken place.
Answer: TRUE
Diff: 2
9) A probability density function is a mathematical way of describing Bayes' theorem.

Answer: FALSE
Diff: 2
Topic: PROBABILITY DISTRIBUTIONS
10) 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.
Answer: TRUE
Diff: 1
11) A probability is a numerical statement about the chance that an event will occur.
Answer: TRUE
Diff: 1
Topic: INTRODUCTION
12) If two events are mutually exclusive, the probability of both events occurring is simply the sum of the
individual probabilities.
Answer: TRUE
Diff: 2
13) Given two statistically dependent events (A,B), the conditional probability of P(A|B) = P(B)/P(AB).
Answer: FALSE
Diff: 2
Topic: STATISTICALLY DEPENDENT EVENTS
14) Given two statistically independent events (A,B), the joint probability of P(AB) = P(A) + P(B).
Answer: FALSE
Diff: 2
15) Given three statistically independent events (A,B,C), the joint probability of P(ABC) = P(A) P(B) P(C).
Answer: TRUE
Diff: 2
16) Given two statistically independent events (A,B), the conditional probability P(A|B) = P(A).
Answer: TRUE
Diff: 2
17) 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.
Answer: TRUE
Diff: 2
18) 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.
Answer: FALSE
Diff: 2
AACSB: Analytic Skills
19) 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.
Answer: FALSE
Diff: 3
20) 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).
Answer: FALSE
Diff: 2
21) If we flip a coin three times, the probability of getting three heads is 0.125.
Answer: TRUE
Diff: 2
22) Consider a standard 52-card deck of cards. The probability of drawing either a seven or a black card is 7/13.
Answer: TRUE
Diff: 2
23) 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.
Answer: FALSE
Diff: 2
24) 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.
Answer: TRUE
Diff: 2
If you draw a numbered ball (N), the probability that this ball is white (W) is 0.60.
Answer: FALSE
Diff: 2
If you draw a lettered ball (L), the probability that this ball is white (W) is 0.571.
Answer: TRUE
Diff: 2
27) The joint probability of two or more independent events occurring is the sum of their marginal or simple
probabilities.
Answer: FALSE
Diff: 2
28) The number of bad checks written at a local store is an example of a discrete random variable.
Answer: TRUE
Diff: 2
Topic: RANDOM VARIABLES
AACSB: Reflective Thinking
29) Given the following distribution:
Outcome
A
B
C
D
Value of
Random Variable Probability
1
.4
2
.3
3
.2
4
.1
The expected value is 3.

Answer: FALSE
Diff: 2

30) 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
0 interruption
1 interruptions
2 interruptions
3 interruptions
Probability
.5
.3
.1
.1
On average, she should expect 0.8 interruptions per hour.

Answer: TRUE
Diff: 2
31) 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
0 interruption
1 interruptions
2 interruptions
3 interruptions
Probability
.4
.3
.2
.1
On average, she should expect 1.0 interruptions per hour.

Answer: TRUE
Diff: 2
32) 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.
Answer: TRUE
Diff: 2
Topic: THE BINOMIAL DISTRIBUTION
33) The standard deviation equals the square of the variance.
Answer: FALSE
Diff: 2
34) The probability of obtaining specific outcomes in a Bernoulli process is described by the binomial probability
distribution.
Answer: TRUE
Diff: 2
35) 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.
Answer: FALSE
Diff: 2
36) The F distribution is a continuous probability distribution that is helpful in testing hypotheses about
variances.
Answer: TRUE
Diff: 2
Topic: THE F DISTRIBUTION
37) The mean and standard deviation of the Poisson distribution are equal.
Answer: FALSE
Diff: 2
Topic: THE POISSON DISTRIBUTION
38) In a normal distribution the Z value represents the number of standard deviations from a value X to the mean.
Answer: TRUE
Diff: 2
Topic: THE NORMAL DISTRIBUTION
39) 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.
Answer: FALSE
Diff: 2
40) 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.
Answer: TRUE
Diff: 2
41) The classical method of determining probability is

A) subjective probability.
B) marginal probability.
C) objective probability.
D) joint probability.
E) conditional probability.
Answer: C
Diff: 2
42) Subjective probability assessments depend on
A) the total number of trials.
B) the relative frequency of occurrence.
C) the number of occurrences of the event.
D) experience and judgment.
E) None of the above
Answer: D
Diff: 1
43) If two events are mutually exclusive, then
A) their probabilities can be added.
B) they may also be collectively exhaustive.
C) the joint probability is equal to 0.
D) if one occurs, the other cannot occur.
E) All of the above
Answer: E
Diff: 2
Topic: MUTUALLY EXCLUSIVE AND COLLECTIVELY EXHAUSTIVE EVENTS and STATISTICALLY
INDEPENDENT EVENTS
44) A ________ is a numerical statement about the likelihood that an event will occur.
A) mutually exclusive construct
B) collectively exhaustive construct
C) variance
D) probability
E) standard deviation
Answer: D
Diff: 1
Topic: INTRODUCTION
45) A conditional probability P(B|A) is equal to its marginal probability P(B) if
A) it is a joint probability.
B) statistical dependence exists.
C) statistical independence exists.
D) the events are mutually exclusive.
E) P(A) = P(B).
Answer: C
Diff: 2

46) The equation P(A|B) = P(AB)/P(B) is
A) the marginal probability.
B) the formula for a conditional probability.
C) the formula for a joint probability.
D) only relevant when events A and B are collectively exhaustive.
Answer: B
Diff: 2
47) 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 ________.
A) relative frequency
B) the classical method
C) the logical method
D) subjective probability
Answer: A
Diff: 1
48) Bayes' theorem is used to calculate
A) revised probabilities.
B) joint probabilities.
C) prior probabilities.
D) subjective probabilities.
E) marginal probabilities.
Answer: A
Diff: 2
49) 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
A) increase by 60 percent.
B) increase by 40 percent.
C) decrease by 60 percent.
D) decrease by 40 percent.
E) be unrelated.
Answer: E
Diff: 2
50) If P(A) = 0.3, P(B) = 0.2, P(A and B) = 0.0 , what can be said about events A and B?
A) They are independent.
B) They are mutually exclusive.
C) They are posterior probabilities.
D) None of the above
E) All of the above
Answer: B
Diff: 2
51) 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?
A) 0.100
B) 0.001
C) 0.300
D) 0.299
E) 0.700
Answer: C
Diff: 1
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?
A) 0.000
B) 1.100
C) 0.198
D) 0.200
E) 0.900
Answer: E
Diff: 2
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?
A) 0.000
B) 1.100
C) 0.198
D) 0.200
E) 0.900
Answer: D
Diff: 2
54) "The probability of event B, given that event A has occurred" is known as a ________ probability.
A) continuous
B) marginal
C) simple
D) joint
E) conditional
Answer: E
Diff: 1
55) When does P(A|B) = P(A)?
A) when A and B are mutually exclusive
B) when A and B are statistically independent
C) when A and B are statistically dependent
D) when A and B are collectively exhaustive
E) when P(B) = 0
Answer: B
Diff: 2
56) 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?
A) The probability of a secretary winning a ticket on the first draw is 6/15.
B) 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.
C) The probability of a consultant winning a ticket on the first draw is 1/3.
D) The probability of two secretaries winning both tickets is 1/7.
E) 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.
Answer: B
Diff: 3
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?
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 secretary winning on the second draw given that a secretary won on the first draw is 2/15.
C) The probability of a consultant winning on the second draw given that a consultant won on the first draw is
5/14.
D) The probability of a partner winning on the second draw given that a secretary won on the first draw is 8/30.
E) None of the above are true.
Answer: A
Diff: 2
10
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?
A) 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.
B) The probability of a secretary and a consultant winning is the same as the probability of a secretary and
secretary winning.
C) 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.
D) The probability that both tickets will be won by partners is the same as the probability that a consultant and
secretary will win.
E) None of the above are true.
Answer: E
Diff: 3
59) 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?
A) 0.45
B) 0.50
C) 0.40
D) 0.05
Answer: C
Diff: 3
DEPENDENT EVENTS
selected at random, what is the probability that the student is enrolled in accounting?
A) 0.20
B) 0.25
C) 0.30
D) 0.50
Answer: C
Diff: 2
11
selected at random, what is the probability that the student is enrolled in statistics?
A) 0.05
B) 0.20
C) 0.25
D) 0.30
Answer: B
Diff: 1
selected at random, what is the probability that the student is enrolled in both statistics and accounting?
A) 0.05
B) 0.06
C) 0.20
D) 0.25
Answer: A
Diff: 2
selected at random and found to be enrolled in statistics, what is the probability that the student is also enrolled
in accounting?
A) 0.05
B) 0.30
C) 0.20
D) 0.25
Answer: D
Diff: 2
12
64) 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?
A) 0.333
B) 0.400
C) 0.833
D) 1.000
E) 0.480
Answer: A
Diff: 2
65) 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?
A) 0.333
B) 0.667
C) 0.800
D) 1.000
E) 0.556
Answer: C
Diff: 2
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?
A) 0.45
B) 0.50
C) 0.55
D) 0.05
Answer: C
Diff: 3
DEPENDENT EVENTS
13
random, what is the probability that the student is not enrolled in accounting?
A) 0.20
B) 0.25
C) 0.30
D) 0.50
Answer: E
Diff: 2
random, what is the probability that the student is not enrolled in statistics?
A) 0.05
B) 0.20
C) 0.25
D) 0.80
Answer: D
Diff: 2
69) 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?
A) 0.05
B) 0.005
C) 0.18
D) 0.20
Answer: A
Diff: 2
14
70) 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)?
A) 0.0100
B) 0.1000
C) 0.2000
D) 0.0025
E) 0.0250
Answer: D
Diff: 2
71) 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?
A) 0.63
B) 0.06
C) 0.07
D) 0.24
E) 0.27
Answer: B
Diff: 2
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?
A) 0.63
B) 0.06
C) 0.07
D) 0.24
E) 0.21
Answer: C
Diff: 2
15
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?
A) 0.63
B) 0.06
C) 0.07
D) 0.24
E) 0.21
Answer: D
Diff: 2
management believes that there is a 70 percent chance that each of these will be successful, and a 30 percent
performed for a new product, what is the probability that the product will be successful if the market research
indicates a success?
A) 0.10
B) 0.90
C) 0.91
D) 0.63
E) 0.09
Answer: C
Diff: 3
75) 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?
A) 0.12
B) 0.60
C) 0.36
D) 0.24
Answer: C
Diff: 2
16
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?
A) 0.40
B) 0.60
C) 0.48
D) 0.24
Answer: C
Diff: 2
DEPENDENT EVENTS
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?
A) 0.16
B) 0.24
C) 0.80
D) 0.36
Answer: A
Diff: 2
performed for a new product, what is the probability that the product will be successful if the market research
indicates a failure?
A) 0.20
B) 0.90
C) 0.91
D) 0.63
E) 0.23
Answer: E
Diff: 3
17
79) Which distribution is helpful in testing hypotheses about variances?

A) binomial distribution
B) F distribution
C) normal distribution
D) Poisson distribution
E) exponential distribution
Answer: B
Diff: 2
80) 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?
A) 0.12
B) 0.60
C) 0.36
D) 0.24
Answer: D
Diff: 2
81) 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?
A) 0.16
B) 0.24
C) 0.80
D) 0.36
Answer: B
Diff: 2
18
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?
A) 0.90
B) 0.54
C) 0.60
D) 0.63
Answer: D
Diff: 2
83) The expected value of a probability distribution is
A) the measure of the spread of the distribution.
B) the variance of the distribution.
C) the average value of the distribution.
D) the probability density function.
E) the range of continuous values from point A to point B, inclusive.
Answer: C
Diff: 1
84) Which of the following is not true for discrete random variables?
A) The expected value is the weighted average of the values.
B) They can assume only a countable number of values.
C) The probability of each value of the random variable must be 0.
D) The probability values always sum up to 1.
E) A binomial random variable is considered discrete.
Answer: C
Diff: 2
85) 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?
A) 1/3
B) 2/3
C) 1
D) 4/3
Answer: C
Diff: 2
19
86) 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?
A) 2
B) 3
C) 4
D) 5
Answer: B
Diff: 2
87) A discrete random variable has a mean of 400 and a variance of 64. What is the standard deviation?
A) 64
B) 8
C) 20
D) 400
Answer: B
Diff: 2
88) Which of the following is not true about continuous random variables?
A) They have an infinite set of values.
B) The area under each of the curves represents probabilities.
C) The entire area under each of the curves equals 1.
D) Some may be described by uniform distributions or exponential distributions.
E) They can only be integer values.
Answer: E
Diff: 2
89) 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?
A) 0.1
B) 0.04
C) 0.137
D) 0.206
E) 0.794
Answer: C
Diff: 3
20
90) 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?
A) 0.85
B) 0.15
C) 0.20
D) 0.411
E) 0.589
Answer: D
Diff: 3
91) Properties of the normal distribution include
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) the random variable can assume only a finite or limited set of values.
E) use in queuing.
Answer: A
Diff: 1
92) Which of the following characteristics is true for a normal probability distribution?
A) The area under the curve is 1.
B) It is symmetrical.
C) The midpoint is also the mean.
D) Sixty-eight percent of the area under the curve lies within one standard deviation of the mean.
E) All of the above are true.
Answer: E
Diff: 2
93) 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?
A) 0
B) 0.023
C) 0.841
D) 0.977
Answer: D
Diff: 2
21
500 and a standard deviation of 50. What is the probability that a student uses fewer than 400 minutes?
A) 0
B) 0.023
C) 0.159
D) 0.977
Answer: B
Diff: 2
500 and a standard deviation of 50. What is the probability that a student uses more than 350 minutes?
A) 0.001
B) 0.999
C) 0.618
D) 0.382
Answer: B
Diff: 2
500 and a standard deviation of 50. What is the probability that a student uses more than 580 minutes?
A) 0.152
B) 0.0548
C) 0.848
D) 0.903
Answer: B
Diff: 2
97) 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?
A) 0
B) 0.023
C) 0.841
D) 0.977
Answer: B
Diff: 2
22
price per square foot for a home is greater than $90?
A) 0
B) 0.023
C) 0.159
D) 0.977
Answer: D
Diff: 2
price per square foot for a home is less than $85?
A) 0.001
B) 0.999
C) 0.618
D) 0.382
Answer: A
Diff: 2
100) 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?
A) 0.152
B) 0.097
C) 0.848
D) 0.945
Answer: D
Diff: 2
23
101) 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?
A) 0
B) 1.000
C) 0.500
D) 1/8
Answer: C
Diff: 2
102) 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?
A) 81.28
B) 92.8
C) 81.82
D) .81954
Answer: B
Diff: 2
103) 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?
A) 0.50
B) 0.20
C) 0.80
D) 1.00
Answer: A
Diff: 2
24
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?
A) 0.84134
B) 0.15866
C) 0.53983
D) 0.46017
Answer: B
Diff: 2
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?
A) 0.2500
B) 0.0625
C) 1.000
D) 0.5000
Answer: D
Diff: 2
106) Queuing Theory makes use of the
A) normal probability distribution.
B) uniform probability distribution.
C) binomial probability distribution.
D) Poisson probability distribution.
Answer: D
Diff: 2
107) The number of cars passing through an intersection in the next five minutes can usually be described by the
A) normal distribution.
B) uniform distribution.
C) exponential distribution.
D) Poisson distribution.
Answer: D
Diff: 2
25
108) 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?
A) 0.0000
B) 0.0661
C) 0.7500
D) 0.1322
Answer: B
Diff: 3
109) 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?
A) 1.000
B) 0.200
C) 0.175
D) 0.825
Answer: E
Diff: 3
110) Which of the following statements concerning the F distribution is true?
A) The F distribution is discrete.
B) The F distribution is symmetrical.
C) The F distribution is useful in modeling customer arrivals.
D) The F distribution is useful in testing hypotheses about variance.
E) The F distribution is interchangeable with the normal distribution for large sample sizes.
Answer: D
Diff: 2
111) What is the F value associated with = 0.05, numerator degrees of freedom (df1) equal to 4, and
denominator degrees of freedom (df2) equal to 9?
A) 3.63
B) 1.80
C) 6.0
D) 0.11
E) 0.18
Answer: A
Diff: 2
26
112) Which of the following characteristics is not true for the exponential distribution?
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) It is used to describe the times between customer arrivals.
E) The variance is the square of the expected value.
Answer: A
Diff: 2
Topic: THE EXPONENTIAL DISTRIBUTION
113) The length of time that it takes the tollbooth attendant to service each driver can typically be described by the
A) normal distribution.
B) uniform distribution.
C) exponential distribution.
D) Poisson distribution.
Answer: C
Diff: 2
114) 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?
A) 1
B) 0.487
C) 0.513
D) 0
E) 0.1
Answer: B
Diff: 3
115) 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?
A) 0.5
B) 0
C) 1
D) 0.368
E) 0.632
Answer: E
Diff: 3
27
116) 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?
A) 0.167
B) 0.223
C) 0.777
D) 0.5
E) 1
Answer: C
Diff: 3
117) 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?
A) 0.632
B) 0.111
C) 0.368
D) 0.632
E) Not enough information given
Answer: C
Diff: 3
118) 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.
Answer: (a) 0.027 (b) 0.210 (c) 0.700 (d) 0.300 (e) 0.300
Diff: 2
28
119) 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.
Male
Female
Positive
Reaction
240
260
Neutral
Reaction
60
220
Negative
Reaction
100
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?
Answer: (a) 100/400 = 0.25 (b) 260/1000 = 0.260 (c) 100/220 = 0.4545
Diff: 2
120) 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?
Answer: (a) 20/300 = 0.067 (b) (280/300)(279/299) = 0.871 (c) (280/300)(20/299) = 0.062
Diff: 2
121) 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?
Answer: (a) 120/200 = 0.60 (b) 60/80 = 0.75 (c) 60/200 = 0.30
Diff: 2
122) 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?
Answer: (a) 0.97(0.97) = 0.9409 (b) 0.03(0.97) + 0.97(0.03) = 0.0582
Diff: 2
29

123) 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?
Answer: P(K|2nd) = 0.06/(.06+.056) = 0.517
Diff: 3
124) 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.
Answer:
Outcome
Probability
Sell 0
0.1
Sell 1
0.2
Sell 2
0.3
Sell 3
0.4
Diff: 2
125) 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
0
1
2
3
More than 3
Probability
0.4
0.3
0.2
0.1
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?
Answer:
(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
Diff: 2
30

126) Fast Service Store has maintained daily sales records on the various size "Cool Drink" sales.
"Cool Drink" Price
$0.50
$0.75
$1.00
$1.25
Total
Number Sold
75
120
125
80
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"?
Answer:
(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
Diff: 3
127) 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?
Answer:
(a) P(r=2) = 0.3020 (b) P(r1) = 0.3758 (c) P(r>1) = 0.6242
Diff: 3
128) 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.
Answer:
(a) P(79<X<85) = 0.68268 (b) P(X>90) = 0.00383 (c) P(X<76) = 0.02275
Diff: 2
31
129) 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.
Answer:
(a) 0.19146 (b) 0.38293 (c) 0.43319 (d) 0.62466 (e) 0.86693
Diff: 3
130) 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?
Answer:
(a) 0.30854 (b) 0.84135 (c) 44 + 1.645(8) = 57.16
Diff: 2
131) Compute the F value based on the following:
(a) df1 = 2, df2 = 4, = 0.01
(b) df1 = 3 df2 = 6, = 0.05
Answer:
(a) 18 (b) 4.76
Diff: 2
132) 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?
Answer:
(a) 0.487 (b) 0.368
Diff: 3
32
133) 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?
Answer:
(a) P(X=4) = 0.1954 (b) P(X=5) = 0.1563
Diff: 3
134) Explain why event probabilities range from 0 to 1.
Answer: 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.
Diff: 2
AACSB: Reflective Thinking
135) Using a standard deck of 52 cards, explain why the situation of drawing a 7 and a club is not collectively
exhaustive.
Answer: It is possible to draw other cards that are non-clubs and also not a 7.
Diff: 2
136) Name five common probability distributions.
Answer: Answers could vary, but may include: binomial, normal, F, exponential, and Poisson.
Diff: 2
Topic: VARIOUS
137) If two events (A,B) are mutually exclusive, what is the probability of event A or event B occurring?
Answer: P(A or B) = P(A) + P(B)
Diff: 2
138) If two events (A,B) are not mutually exclusive, what is the probability of event A or event B occurring?
Answer: P(A or B) = P(A) + P(B) - P(A and B)
Diff: 2
139) If two events (A,B) are independent, what is their joint probability?
Answer: P(AB) = P(A) P(B)
Diff: 2
140) If two events (A,B) are dependent, what is the conditional probability of P(A|B)?
Answer: P(A|B) = P(AB)|P(B)
Diff: 2
33
141) If two events (A,B) are independent, then the conditional probability of P(A|B) = ________.
Answer: P(A)
Diff: 2
142) Explain what a discrete random variable is.
Answer: 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.
Diff: 2
143) The exponential distribution often describes ________.
Answer: the time required to service a customer
Diff: 2
144) List the two parameters of the normal distribution.
Answer: mean () and standard deviation ()
Diff: 2
145) In what way is the F distribution often used?
Answer: It is helpful in testing hypotheses about variances.
Diff: 2
146) List the parameter(s) of the Poisson distribution.
Answer: the mean and the variance
Diff: 2
34

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Quantitative Analysis for Management, 11e (Render)

Chapter 2 Probability Concepts and Applications

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

The expected value is 3.

AACSB: Analytic Skills

On average, she should expect 0.8 interruptions per hour.

On average, she should expect 1.0 interruptions per hour.

41) The classical method of determining probability is

Topic: STATISTICALLY INDEPENDENT EVENTS

79) Which distribution is helpful in testing hypotheses about variances?

AACSB: Analytic Skills

(a) What is the expected number of breakdowns in any given day?

AACSB: Analytic Skills

Assuming that past performance is a good indicator of future sales,

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