Chapter 06Discrete Probability Distributions
True / False Questions1.A random variable is a function or rule
that assigns a numerical value to each outcome in the sample space
of a stochastic (chance) experiment.TrueFalse
2.A discrete random variable has a countable number of distinct
values.TrueFalse
3.The expected value of a discrete random variable E(X) is the
sum of all X values weighted by their respective
probabilities.TrueFalse
4.A discrete distribution can be described by its probability
density function (PDF) or by its cumulative distribution function
(CDF).TrueFalse
5.A random variable may be discrete or continuous, but not
both.TrueFalse
6.To describe the number of blemishes per sheet of white bond
paper, we would use a discrete uniform distribution.TrueFalse
7.The outcomes for the sum of two dice can be described as a
discrete uniform distribution.TrueFalse
8.A discrete binomial distribution is skewed right when >
.50.TrueFalse
9.When = .70 the discrete binomial distribution is negatively
skewed.TrueFalse
10.The Poisson distribution describes the number of occurrences
within a randomly chosen unit of time or space.TrueFalse
11.The Poisson distribution can be skewed either left or right,
depending on .TrueFalse
12.Although the shape of the Poisson distribution is positively
skewed, it becomes more nearly symmetric as its mean becomes
larger.TrueFalse
13.As a rule of thumb, the Poisson distribution can be used to
approximate a binomial distribution when n 20 and .05.TrueFalse
14.The hypergeometric distribution is skewed right.TrueFalse
15.The hypergeometric distribution assumes that the probability
of a success remains the same from one trial to the
next.TrueFalse
16.The hypergeometric distribution is not applicable if sampling
is done with replacement.TrueFalse
17.As a rule of thumb, the binomial distribution can be used to
approximate the hypergeometric distribution whenever the population
is at least 20 times as large as the sample.TrueFalse
18.An example of a geometric random variable is the number of
pine trees with pine beetle infestation in a random sample of 15
pine trees in Colorado.TrueFalse
19.Calculating the probability of getting three aces in a hand
of five cards dealt from a deck of 52 cards would require the use
of a hypergeometric distribution.TrueFalse
20.The Poisson distribution is appropriate to describe the
number of babies born in a small hospital on a given
day.TrueFalse
21.The gender of a randomly chosen unborn child is a Bernoulli
event.TrueFalse
22.The Poisson distribution has only one parameter.TrueFalse
23.The standard deviation of a Poisson random variable is the
square root of its mean.TrueFalse
24.Customer arrivals per unit of time would tend to follow a
binomial distribution.TrueFalse
25.The two outcomes (success, failure) in the Bernoulli model
are equally likely.TrueFalse
26.The expected value of a random variable is its
mean.TrueFalse
Multiple Choice Questions27.A discrete probability
distribution:
A.is a listing of all possible values of the random
variable.
B.assigns a probability to each possible value of the random
variable.
C.can assume values between -1 and +1.
D.is independent of the parameters of the distribution.
28.The number of male babies in a sample of 10 randomly chosen
babies is a:
A.continuous random variable.
B.Poisson random variable.
C.binary random variable.
D.binomial random variable.
29.A discrete random variable:
A.can be treated as continuous when it has a large range of
values.
B.cannot be treated as continuous.
C.is best avoided if at all possible.
D.is usually uniformly distributed.
30.Which is not a discrete random variable?
A.The number of defects in a 4 8 sheet of plywood
B.The number of female passengers who board a plane
C.The time until failure of a vehicle headlamp
D.The number of correct answers on a statistics exam
31.Which is a not a discrete random variable?
A.The number of births in a hospital on a given day
B.The number of fives obtained in four rolls of a die
C.The hourly earnings of a call center employee in Boston
D.The number of applicants applying for a civil service job
32.Which statement is incorrect?
A.The Poisson distribution is always skewed right.
B.The binomial distribution may be skewed left or right.
C.The discrete uniform distribution is always symmetric.
D.The hypergeometric distribution is symmetric.
33.The random variable X is the number of shots it takes before
you make the first free throw in basketball. Assuming the
probability of success (making a free throw) is constant from trial
to trial, what type of distribution does X follow?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
34.Which probability model is most nearly appropriate to
describe the number of burned-out fluorescent tubes in a classroom
with 12 fluorescent tubes, assuming a constant probability of a
burned-out tube?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
35.Which distribution is most nearly appropriate to describe the
number of fatalities in Texas in a given year due to poisonous
snakebites?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
36.Which model would you use to describe the probability that a
call-center operator will make the first sale on the third call,
assuming a constant probability of making a sale?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
37.In a randomly chosen week, which probability model would you
use to describe the number of accidents at the intersection of two
streets?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
38.Which model best describes the number of nonworking web URLs
("This page cannot be displayed") you encounter in a randomly
chosen minute while surfing websites for Florida vacation rental
condos?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
39.Which probability model would you use to describe the number
of damaged printers in a random sample of 4 printers taken from a
shipment of 28 printers that contains 3 damaged printers?
A.Poisson
B.Hypergeometric
C.Binomial
D.Uniform
40.Which model best describes the number of incorrect fare
quotations by a well-trained airline ticket agent between 2 p.m.
and 3 p.m. on a particular Thursday.
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
41.Which model best describes the number of blemishes per sheet
of white bond paper?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
42.To ensure quality, customer calls for airline fare quotations
are monitored at random. On a particular Thursday afternoon, ticket
agent Bob gives 40 fare quotations, of which 4 are incorrect. In a
random sample of 8 of these customer calls, which model best
describes the number of incorrect quotations Bob will make?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
43.The number of people injured in rafting expeditions on the
Colorado River on a randomly chosen Thursday in August is best
described by which model?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
44.On a particular Thursday in August, 40 Grand Canyon tourists
enter a drawing for a free mule ride. Ten of the entrants are
European tourists. Five entrants are selected at random to get the
free mule ride. Which model best describes the number of European
tourists in the random sample?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
45.Which model best describes the number of births in a hospital
until the first twins are delivered?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
46.On a randomly chosen Wednesday, which probability model would
you use to describe the number of convenience store robberies in
Los Angeles?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
47.Which probability model would you use to describe the number
of customers served at a certain California Pizza Kitchen until the
first customer orders split pea soup?
A.Binomial
B.Geometric
C.Uniform
D.Poisson
48.Which distribution has a mean of 5?
A.Poisson with = 25.
B.Binomial with n = 200, = .05
C.Hypergeometric with N = 100, n = 10, s = 50
49.Of the following, the one that most resembles a Poisson
random variable is the number of:
A.heads in 200 flips of a fair coin.
B.annual power failures at your residence.
C.face cards in a bridge hand of 13 cards.
D.defective CDs in a spool containing 15 CDs.
50.A charity raffle prize is $1,000. The charity sells 4,000
raffle tickets. One winner will be selected at random. At what
ticket price would a ticket buyer expect to break even?
A.$0.50
B.$0.25
C.$0.75
D.$1.00
51.A die is rolled. If it rolls to a 1, 2, or 3 you win $2. If
it rolls to a 4, 5, or 6 you lose $1. Find the expected
winnings.
A.$0.50
B.$3.00
C.$1.50
D.$1.00
52.A fair die is rolled. If it comes up 1 or 2 you win $2. If it
comes up 3, 4, 5, or 6 you lose $1. Find the expected winnings.
A.$0.00
B.$1.00
C.$0.50
D.$0.25
53.A carnival has a game of chance: a fair coin is tossed. If it
lands heads you win $1.00 and if it lands tails you lose $0.50. How
much should a ticket to play this game cost if the carnival wants
to break even?
A.$0.25
B.$0.50
C.$0.75
D.$1.00
54.Ephemeral Services Corporation (ESCO) knows that nine other
companies besides ESCO are bidding for a $900,000 government
contract. Each company has an equal chance of being awarded the
contract. If ESCO has already spent $100,000 in developing its
bidding proposal, what is its expected net profit?
A.$100,000
B.$90,000
C.-$10,000
D.$0
55.The discrete random variable X is the number of students that
show up for Professor Smith's office hours on Monday afternoons.
The table below shows the probability distribution for X. What is
the expected value E(X) for this distribution?
A.1.2
B.1.0
C.1.5
D.2.0
56.The discrete random variable X is the number of students that
show up for Professor Smith's office hours on Monday afternoons.
The table below shows the probability distribution for X. What is
the probability that at least 1 student comes to office hours on
any given Monday?
A..30
B..40
C..50
D..60
57.The discrete random variable X is the number of students that
show up for Professor Smith's office hours on Monday afternoons.
The table below shows the probability distribution for X. What is
the probability that fewer than 2 students come to office hours on
any given Monday?
A..10
B..40
C..70
D..90
58.The discrete random variable X is the number of passengers
waiting at a bus stop. The table below shows the probability
distribution for X. What is the expected value E(X) for this
distribution?
A.1.1
B.1.3
C.1.7
D.1.9
59.Given the following probability distribution, what is the
expected value of the random variable X?
A.175
B.150
C.200
D.205
60.Which of the following characterizes a Bernoulli process?
A.A random experiment that has only two outcomes.
B.The probability of "success" varies with each trial.
C.Either outcome has the same chance of occurrence.
D.The "success" must be a desirable outcome.
61.The binomial distribution describes the number of:
A.trials to obtain the first "success" in a Bernoulli
process.
B.trials to obtain n "successes" in a Bernoulli process.
C."successes" or "failures" in a Bernoulli process.
D."successes" in n Bernoulli trials.
62.Which of the following is not a requirement of a binomial
distribution?
A.Constant probability of success
B.Only two possible Bernoulli outcomes
C.Fixed number of trials
D.Equally likely outcomes
63.The binomial distribution is symmetrical when:
A. = 1 and 1 - = 0.
B. = and 1 - = .
C. = and 1 - = .
D. = 0 and 1 - = 1.
64.The variance will reach a maximum in a binomial distribution
when:
A. = 1 and 1 - = 0.
B. = and 1 - = .
C. = and 1 - = .
D. = 0 and 1 - = 1.
65.Which distribution is most strongly right-skewed?
A.Binomial with n = 50, = .70
B.Binomial with n = 50, = .90
C.Binomial with n = 50, = .40
D.Binomial with n = 50, = .10
66.A random variable is binomially distributed with n = 16 and =
.40. The expected value and standard deviation of the variables
are:
A.2.00 and 1.24
B.4.80 and 4.00
C.6.40 and 1.96
D.2.00 and 1.20
67.The expected value (mean) of a binomial variable is 15. The
number of trials is 20. The probability of "success" is:
A..25
B..50
C..75
D..30
68.If 90 percent of automobiles in Orange County have both
headlights working, what is the probability that in a sample of
eight automobiles, at least seven will have both headlights
working?
A..6174
B..3826
C..8131
D..1869
69.In Quebec, 90 percent of the population subscribes to the
Roman Catholic religion. In a random sample of eight Quebecois,
find the probability that the sample contains at least five Roman
Catholics.
A..0050
B..0331
C..9950
D..9619
70.Hardluck Harry has a batting average of .200 (i.e., a 20
percent chance of a hit each time he's at bat). Scouts for a rival
baseball club secretly observe Harry's performance in 12 random
times at bat. What is the probability that Harry will get more than
2 hits?
A..2055
B..2362
C..7946
D..4417
71.The probability that a visitor to an animal shelter will
adopt a dog is .20. Out of nine visits, what is the probability
that at least one dog will be adopted?
A..8658
B..3020
C..5639
D..1342
72.Based on experience, 60 percent of the women who request a
pregnancy test at a certain clinic are actually pregnant. In a
random sample of 12 women, what is the probability that at least 10
are pregnant?
A..0639
B..1424
C..0196
D..0835
73.If 5 percent of automobiles in Oakland County have one
burned-out headlight, what is the probability that, in a sample of
10 automobiles, none will have a burned-out headlight?
A..5987
B..3151
C..0116
D..1872
74.Jankord Jewelers permits the return of their diamond wedding
rings, provided the return occurs within two weeks. Typically, 10
percent are returned. If eight rings are sold today, what is the
probability that fewer than three will be returned?
A..9950
B..9619
C..0331
D..1488
75.The probability that an Oxnard University student is carrying
a backpack is .70. If 10 students are observed at random, what is
the probability that fewer than 7 will be carrying backpacks?
A..3504
B..2001
C..6177
D..2668
76.An insurance company is issuing 16 car insurance policies.
Suppose the probability for a claim during a year is 15 percent. If
the binomial probability distribution is applicable, then the
probability that there will be at least two claims during the year
is equal to:
A..5615
B..2775
C..7161
D..0388
77.A random variable X is distributed binomially with n = 8 and
= 0.70. The standard deviation of the variable X is
approximately:
A.0.458
B.2.828
C.1.680
D.1.296
78.Suppose X is binomially distributed with n = 12 and = .20.
The probability that X will be less than or equal to 3 is:
A..5584
B..7946
C..2362
D..7638
79.Which Excel function would generate a single random X value
for a binomial random variable with parameters n = 16 and =
.25?
A.=BINOM.DIST(RAND(), 16, .25, 0)
B.=BINOM.DIST(0, 16, .25, RAND())
C.=BINOM.INV(16, .25, RAND())
D.=BINOM.INV(0, 16, .25, RAND())
80.A network has three independent file servers, each with 90
percent reliability. The probability that the network will be
functioning correctly (at least one server is working) at a given
time is:
A.99.9 percent.
B.97.2 percent.
C.95.9 percent.
D.72.9 percent.
81.Which statement concerning the binomial distribution is
correct?
A.Its PDF covers all integer values of X from 0 to n.
B.Its PDF is the same as its CDF when = .50.
C.Its CDF shows the probability of each value of X.
D.Its CDF is skewed right when < .50.
82.Historically, 2 percent of the stray dogs in Southfield are
unlicensed. On a randomly chosen day, the Southfield city animal
control officer picks up seven stray dogs. What is the probability
that fewer than two will be unlicensed?
A..8681
B..9921
C..3670
D..0076
83.The domain of X in a Poisson probability distribution is
discrete and can include:
A.any real X value.
B.any integer X value.
C.any nonnegative integer X value.
D.any X value except zero.
84.On Saturday morning, calls arrive at TicketMaster at a rate
of 108 calls per hour. What is the probability of fewer than three
calls in a randomly chosen minute?
A..1607
B..8913
C..2678
D..7306
85.On average, a major earthquake (Richter scale 6.0 or above)
occurs three times a decade in a certain California county. Find
the probability that at least one major earthquake will occur
within the next decade.
A..7408
B..1992
C..1494
D..9502
86.On average, an IRS auditor discovers 4.7 fraudulent income
tax returns per day. On a randomly chosen day, what is the
probability that she discovers fewer than two?
A..0518
B..0427
C..1005
D..1523
87.On a Sunday in April, dog bite victims arrive at Carver
Memorial Hospital at a historical rate of 0.6 victim per day. On a
given Sunday in April, what is the probability that exactly two dog
bite victims will arrive?
A..0875
B..0902
C..0988
D..0919
88.If tubing averages 16 defects per 100 meters, what is the
probability of finding exactly 2 defects in a randomly chosen
10-meter piece of tubing?
A..8795
B..2674
C..3422
D..2584
89.Cars are arriving at a toll booth at a rate of four per
minute. What is the probability that exactly eight cars will arrive
in the next two minutes?
A.0.0349
B.0.1396
C.0.9666
D.0.0005
90.Arrival of cars per minute at a toll booth may be
characterized by the Poisson distribution if:
A.the arrivals are independent.
B.no more than one arrival can occur in a minute.
C.there is only one lane leading to the booth.
D.the mean arrival rate is at least 30.
91.The coefficient of variation for a Poisson distribution with
= 5 is:
A.35.2 percent.
B.58.9 percent.
C.44.7 percent.
D.31.1 percent.
92.The coefficient of variation for a Poisson distribution with
= 4 is:
A.35.2 percent.
B.58.9 percent.
C.50.0 percent.
D.26.4 percent.
93.For which binomial distribution would a Poisson approximation
be unacceptable?
A.n = 30, = 0.02
B.n = 50, = 0.03
C.n = 200, = 0.10
D.n = 500, = 0.01
94.For which binomial distribution would a Poisson approximation
be acceptable?
A.n = 60, = 0.08
B.n = 100, = 0.15
C.n = 40, = 0.03
D.n = 20, = 0.20
95.For which binomial distribution would a Poisson approximation
not be acceptable?
A.n = 35, = 0.07
B.n = 95, = 0.01
C.n = 80, = 0.02
D.n = 50, = 0.03
96.The true proportion of accounts receivable with some kind of
error is .02 for Venal Enterprises. If an auditor randomly samples
200 accounts receivable, what is the approximate Poisson
probability that fewer than two will contain errors?
A..1038
B..0916
C..1465
D..0015
97.The probability that a rental car will be stolen is 0.0004.
If 3500 cars are rented, what is the approximate Poisson
probability that 2 or fewer will be stolen?
A..3452
B..2417
C..5918
D..8335
98.The probability that a customer will use a stolen credit card
to make a purchase at a certain Target store is 0.003. If 400
purchases are made in a given day, what is the approximate Poisson
probability that 4 or fewer will be with stolen cards?
A..0053
B..0076
C..9923
D..0555
99.The probability that a ticket holder will miss a flight is
.005. If 180 passengers take the flight, what is the approximate
Poisson probability that at least 2 will miss the flight?
A..9372
B..0628
C..1647
D..2275
100.The probability that a certain daily flight's departure from
ORD to LAX is delayed is .02. Over six months, this flight departs
180 times. What is the approximate Poisson probability that it will
be delayed fewer than 2 times?
A..4471
B..3028
C..1257
D..1771
101.If X is a discrete uniform random variable ranging from 0 to
12, find P(X 10).
A..1126
B..1666
C..2308
D..2500
102.If X is a discrete uniform random variable ranging from one
to eight, find P(X < 6).
A..6250
B..5000
C..7500
D..3750
103.If X is a discrete uniform random variable ranging from one
to eight, its mean is:
A.4.0
B.4.5
C.5.0
D.5.5
104.If X is a discrete uniform random variable ranging from 12
to 24, its mean is:
A.18.5.
B.16.0.
C.18.0.
D.19.5.
105.At Ersatz University, the graduating class of 480 includes
96 guest students from Latvia. A sample of 10 students is selected
at random to attend a dinner with the Board of Governors. Use the
binomial model to obtain the approximate hypergeometric probability
that the sample contains at least three Latvian students.
A..3222
B..1209
C..8791
D..6778
106.There are 90 passengers on a commuter flight from SFO to
LAX, of whom 27 are traveling on business. In a random sample of
five passengers, use the binomial model to find the approximate
hypergeometric probability that there is at least one business
passenger.
A..3087
B..1681
C..3602
D..8319
107.Use the binomial model to find the approximate
hypergeometric probability of at least two damaged flash drives in
a sample of five taken from a shipment of 150 that contains 30
damaged flash drives.
A.0.9421
B.0.0579
C.0.7373
D.0.2627
108.On a particular day, 112 of 280 passengers on a particular
DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding
passes. In a random sample of eight passengers, use the binomial
model to find the approximate hypergeometric probability that four
will have used the e-ticket check-in kiosk to obtain boarding
passes.
A..2322
B..8263
C..2926
D..5613
109.A clinic employs nine physicians. Five of the physicians are
female. Four patients arrive at once. Assuming the doctors are
assigned randomly to patients, what is the probability that all of
the assigned physicians are female?
A..0397
B..0295
C..0808
D..0533
110.There is a .02 probability that a customer's Visa charge
will be rejected at a certain Target store because the transaction
exceeds the customer's credit limit. What is the probability that
the first such rejection occurs on the third Visa transaction?
A..0192
B..0025
C..0247
D..0200
111.Ten percent of the corporate managers at Axolotl Industries
majored in humanities. What is the probability that the first
humanities major is the fifth manager you meet?
A..0656
B..8561
C..5904
D..4095
112.Ten percent of the corporate managers at Axolotl Industries
majored in humanities. What is the expected number of managers to
be interviewed until finding the first one with a humanities
major?
A.15
B.20
C.10
D.17
113.When you send out a resume, the probability of being called
for an interview is .20. What is the probability that the first
interview occurs on the fourth resume that you send out?
A..4096
B..1024
C..2410
D..0016
114.When you send out a resume, the probability of being called
for an interview is .20. What is the expected number of resumes you
send out until you get the first interview?
A.5
B.7
C.10
D.12
115.When you send out a resume, the probability of being called
for an interview is .20. What is the probability that you get your
first interview within the first five resumes that you send
out?
A..6723
B..1024
C..2410
D..0016
116.There is a .02 probability that a customer's Visa charge
will be rejected at a certain Target store because the transaction
exceeds the customer's credit limit. What is the probability that
the first such rejection occurs within the first 20 Visa
transactions?
A..1362
B..4000
C..3324
D..4538
117.There is a .02 probability that a customer's Visa charge
will be rejected at a certain Target store because the transaction
exceeds the customer's credit limit. What is the expected number of
Visa transactions until the first one is rejected?
A.10
B.20
C.50
D.98
118.The geometric distribution best describes:
A.the number of successes in a sample of n trials.
B.the number of trials until the first success.
C.the number of events in a given unit of time.
D.the process of sampling without replacement.
119.The CDF for the geometric distribution shows:
A.the probability of success in a random experiment consisting
of n independent trials.
B.the probability that the first success will occur within a
given number of trials.
C.the probability that no success will be obtained in a given
Bernoulli trial.
D.the probability of more than one success in the first n
trials.
120.If the probability of success is .25, what is the
probability of obtaining the first success within the first three
trials?
A..4218
B..5781
C..1406
D..2228
121.If the probability of success is .30, what is the
probability of obtaining the first success within the first five
trials?
A..0024
B..8319
C..1681
D..9976
122.A project has three independent stages that must be
completed in sequence. The time to complete each stage is a random
variable. The expected times to complete the stages are 1 = 23, 2 =
11, 3 = 17. The expected project completion time is:
A.51.
B.23.
C.40.
D.32.
123.A project has 3 independent stages that must be completed in
sequence. The time to complete each stage is a random variable. The
standard deviations of the completion times for the stages are 1 =
5, 2 = 4, 3 = 6. The standard deviation of the overall project
completion time is:
A.8.77
B.15.0
C.14.2
D.9.24
124.A stock portfolio consists of two stocks X and Y. Their
daily closing prices are independent random variables with standard
deviations X = 2.51 and Y = 5.22. What is the standard deviation of
the sum of the closing prices of these two stocks?
A.33.55
B.6.48
C.7.73
D.5.79
125.A stock portfolio consists of two stocks X and Y. Their
daily closing prices are correlated random variables with variances
X2 = 3.51 and Y2 = 5.22, and covariance XY = -1.55. What is the
standard deviation of the sum of the closing prices of these two
stocks?
A.5.63
B.7.18
C.8.73
D.2.68
126.The expected value of a random variable X is 140 and the
standard deviation is 14. The standard deviation of the random
variable Y = 3X - 10 is:
A.42
B.6.48
C.14
D.32
127.The expected value of a random variable X is 10 and the
standard deviation is 2. The standard deviation of the random
variable Y = 2X - 10 is:
A.2
B.4
C.-10
D.-6
Chapter 06 Discrete Probability Distributions Answer Key
True / False Questions1.A random variable is a function or rule
that assigns a numerical value to each outcome in the sample space
of a stochastic (chance) experiment.TRUEReview definition of random
variable.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-01 Define a discrete random variable.Topic: Discrete
Distributions
2.A discrete random variable has a countable number of distinct
values.TRUEReview definition of random variable.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-01 Define a discrete random variable.Topic: Discrete
Distributions
3.The expected value of a discrete random variable E(X) is the
sum of all X values weighted by their respective
probabilities.TRUEReview definition of expected value.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
4.A discrete distribution can be described by its probability
density function (PDF) or by its cumulative distribution function
(CDF).TRUEReview definition of PDF and CDF.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-03 Define probability distribution; PDF; and
CDF.Topic: Discrete Distributions
5.A random variable may be discrete or continuous, but not
both.TRUEReview definition of discrete and continuous.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-01 Define a discrete random variable.Topic: Discrete
Distributions
6.To describe the number of blemishes per sheet of white bond
paper, we would use a discrete uniform distribution.FALSENot all X
values would be equally likely (Poisson distribution would be
better).
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
7.The outcomes for the sum of two dice can be described as a
discrete uniform distribution.FALSEThe sum of two uniforms is a
triangular distribution, as shown in the textbook example.
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-04 Know the mean and variance of a uniform discrete
model.Topic: Uniform Distribution
8.A discrete binomial distribution is skewed right when >
.50.FALSEMost outcomes would be on the right, so a longer left tail
exists.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
9.When = .70 the discrete binomial distribution is negatively
skewed.TRUEMost outcomes would be on the right, so a longer left
tail exists.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
10.The Poisson distribution describes the number of occurrences
within a randomly chosen unit of time or space.TRUEPoisson
describes events per unit of time.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
11.The Poisson distribution can be skewed either left or right,
depending on .FALSEPoisson is always right-skewed.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
12.Although the shape of the Poisson distribution is positively
skewed, it becomes more nearly symmetric as its mean becomes
larger.TRUEAlthough always right-skewed, the Poisson approaches a
normal as the mean increases.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
13.As a rule of thumb, the Poisson distribution can be used to
approximate a binomial distribution when n 20 and .05.TRUEThe
Poisson is a better approximation to binomial when n is large and
is small.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
14.The hypergeometric distribution is skewed right.FALSEThe
hypergeometric is skewed right if s/N < .50 (and
conversely).
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
15.The hypergeometric distribution assumes that the probability
of a success remains the same from one trial to the next.FALSEThe
point of the hypergeometric is that is not constant.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
16.The hypergeometric distribution is not applicable if sampling
is done with replacement.TRUEThe hypergeometric is used when there
is no replacement in sampling from a finite population
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
17.As a rule of thumb, the binomial distribution can be used to
approximate the hypergeometric distribution whenever the population
is at least 20 times as large as the sample.TRUEThe rule is to use
the approximation if n/N < .05.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
18.An example of a geometric random variable is the number of
pine trees with pine beetle infestation in a random sample of 15
pine trees in Colorado.FALSEThis is a binomial experiment, assuming
is constant.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
19.Calculating the probability of getting three aces in a hand
of five cards dealt from a deck of 52 cards would require the use
of a hypergeometric distribution.TRUEThis is a hypergeometric
experiment (no replacement).
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
20.The Poisson distribution is appropriate to describe the
number of babies born in a small hospital on a given day.TRUEEvents
per unit of time with no clear upper limit.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
21.The gender of a randomly chosen unborn child is a Bernoulli
event.TRUETwo outcomes (0 or 1).
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Bernoulli Distribution
22.The Poisson distribution has only one parameter.TRUEThe one
parameter is the mean.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
23.The standard deviation of a Poisson random variable is the
square root of its mean.TRUEReview Poisson model.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
24.Customer arrivals per unit of time would tend to follow a
binomial distribution.FALSEThis would be a Poisson (arrivals per
unit of time).
AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
25.The two outcomes (success, failure) in the Bernoulli model
are equally likely.FALSEThe probability of success need not be
.50.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Bernoulli Distribution
26.The expected value of a random variable is its mean.TRUEThe
mean is another name for expected value.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
Multiple Choice Questions27.A discrete probability
distribution:
A.is a listing of all possible values of the random
variable.
B.assigns a probability to each possible value of the random
variable.
C.can assume values between -1 and +1.
D.is independent of the parameters of the distribution.
A discrete PDF assigns a probability to each X value.
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-03 Define probability distribution; PDF; and
CDF.Topic: Discrete Distributions
28.The number of male babies in a sample of 10 randomly chosen
babies is a:
A.continuous random variable.
B.Poisson random variable.
C.binary random variable.
D.binomial random variable.
Constant probability of success in n trials.
AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Binomial Distribution
29.A discrete random variable:
A.can be treated as continuous when it has a large range of
values.
B.cannot be treated as continuous.
C.is best avoided if at all possible.
D.is usually uniformly distributed.
Review definitions of discrete distributions.
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-01 Define a discrete random variable.Topic: Discrete
Distributions
30.Which is not a discrete random variable?
A.The number of defects in a 4 8 sheet of plywood
B.The number of female passengers who board a plane
C.The time until failure of a vehicle headlamp
D.The number of correct answers on a statistics exam
Time is continuous.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-01 Define a discrete random variable.Topic: Discrete
Distributions
31.Which is a not a discrete random variable?
A.The number of births in a hospital on a given day
B.The number of fives obtained in four rolls of a die
C.The hourly earnings of a call center employee in Boston
D.The number of applicants applying for a civil service job
Someone's earnings would be more like a continuous
measurement.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-01 Define a discrete random variable.Topic: Discrete
Distributions
32.Which statement is incorrect?
A.The Poisson distribution is always skewed right.
B.The binomial distribution may be skewed left or right.
C.The discrete uniform distribution is always symmetric.
D.The hypergeometric distribution is symmetric.
Review characteristics of the distributions. A hypergeometric is
symmetric only if s/N = .50.
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
33.The random variable X is the number of shots it takes before
you make the first free throw in basketball. Assuming the
probability of success (making a free throw) is constant from trial
to trial, what type of distribution does X follow?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Geometric model describes the number of trials until the first
success.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Geometric Distribution
(Optional)
34.Which probability model is most nearly appropriate to
describe the number of burned-out fluorescent tubes in a classroom
with 12 fluorescent tubes, assuming a constant probability of a
burned-out tube?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
n = 12 Bernoulli trials with fixed probability of success would
be a binomial model.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Binomial Distribution
35.Which distribution is most nearly appropriate to describe the
number of fatalities in Texas in a given year due to poisonous
snakebites?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Events per unit of time with no clear upper limit would resemble
a Poisson distribution.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
36.Which model would you use to describe the probability that a
call-center operator will make the first sale on the third call,
assuming a constant probability of making a sale?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Geometric describes the number of trials to first success.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Geometric Distribution
(Optional)
37.In a randomly chosen week, which probability model would you
use to describe the number of accidents at the intersection of two
streets?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Events per unit of time with no clear upper limit would resemble
a Poisson distribution.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
38.Which model best describes the number of nonworking web URLs
("This page cannot be displayed") you encounter in a randomly
chosen minute while surfing websites for Florida vacation rental
condos?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Events per unit of time with no clear upper limit would resemble
a Poisson distribution.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
39.Which probability model would you use to describe the number
of damaged printers in a random sample of 4 printers taken from a
shipment of 28 printers that contains 3 damaged printers?
A.Poisson
B.Hypergeometric
C.Binomial
D.Uniform
Sampling (n = 4 printers) without replacement with known number
of "successes" (s = 3 damaged printers) in the population (N = 28
printers).
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Hypergeometric
Distribution
40.Which model best describes the number of incorrect fare
quotations by a well-trained airline ticket agent between 2 p.m.
and 3 p.m. on a particular Thursday.
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Events per unit of time with no clear upper limit would resemble
a Poisson distribution.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
41.Which model best describes the number of blemishes per sheet
of white bond paper?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Events per unit of area with no clear upper limit would resemble
a Poisson distribution.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
42.To ensure quality, customer calls for airline fare quotations
are monitored at random. On a particular Thursday afternoon, ticket
agent Bob gives 40 fare quotations, of which 4 are incorrect. In a
random sample of 8 of these customer calls, which model best
describes the number of incorrect quotations Bob will make?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Sampling (n = 8 calls selected) without replacement with known
number of "successes" (s = 4 incorrect quotes) in the population (N
= 40 quotes).
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Hypergeometric
Distribution
43.The number of people injured in rafting expeditions on the
Colorado River on a randomly chosen Thursday in August is best
described by which model?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Independent events per unit of time with no clear upper limit
would be Poisson.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
44.On a particular Thursday in August, 40 Grand Canyon tourists
enter a drawing for a free mule ride. Ten of the entrants are
European tourists. Five entrants are selected at random to get the
free mule ride. Which model best describes the number of European
tourists in the random sample?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Sampling (n = 5 tourists selected) without replacement with
known number of "successes" (s = 10 Europeans) in the population (N
= 40).
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Hypergeometric
Distribution
45.Which model best describes the number of births in a hospital
until the first twins are delivered?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Geometric distribution describes the number of trials until the
first success.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Geometric Distribution
(Optional)
46.On a randomly chosen Wednesday, which probability model would
you use to describe the number of convenience store robberies in
Los Angeles?
A.Binomial
B.Poisson
C.Hypergeometric
D.Geometric
Events per unit of time with no clear upper limit.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Poisson Distribution
47.Which probability model would you use to describe the number
of customers served at a certain California Pizza Kitchen until the
first customer orders split pea soup?
A.Binomial
B.Geometric
C.Uniform
D.Poisson
Geometric distribution describes the number of trials until the
first success.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-10 Select an appropriate discrete probability
distribution from problem context.Topic: Geometric Distribution
(Optional)
48.Which distribution has a mean of 5?
A.Poisson with = 25.
B.Binomial with n = 200, = .05
C.Hypergeometric with N = 100, n = 10, s = 50
Review model parameters. The hypergeometric mean is ns/N =
(10)(50)/100 = 5.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
49.Of the following, the one that most resembles a Poisson
random variable is the number of:
A.heads in 200 flips of a fair coin.
B.annual power failures at your residence.
C.face cards in a bridge hand of 13 cards.
D.defective CDs in a spool containing 15 CDs.
Independent arrivals per unit of time with no clear upper limit
would be Poisson.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
50.A charity raffle prize is $1,000. The charity sells 4,000
raffle tickets. One winner will be selected at random. At what
ticket price would a ticket buyer expect to break even?
A.$0.50
B.$0.25
C.$0.75
D.$1.00
Expected winning is (1/4000) $1000 = $0.25.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
51.A die is rolled. If it rolls to a 1, 2, or 3 you win $2. If
it rolls to a 4, 5, or 6 you lose $1. Find the expected
winnings.
A.$0.50
B.$3.00
C.$1.50
D.$1.00
E(X) = (3/6) $2 + (3/6) (-$1) = $0.50.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
52.A fair die is rolled. If it comes up 1 or 2 you win $2. If it
comes up 3, 4, 5, or 6 you lose $1. Find the expected winnings.
A.$0.00
B.$1.00
C.$0.50
D.$0.25
E(X) = (2/6) $2 + (4/6) (-$1) = $0.6667 - $0.6667 = 0.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
53.A carnival has a game of chance: a fair coin is tossed. If it
lands heads you win $1.00 and if it lands tails you lose $0.50. How
much should a ticket to play this game cost if the carnival wants
to break even?
A.$0.25
B.$0.50
C.$0.75
D.$1.00
E(X) = (.5) $1 + (.5) (-$.50) = $0.50 - $0.25 = $0.25.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
54.Ephemeral Services Corporation (ESCO) knows that nine other
companies besides ESCO are bidding for a $900,000 government
contract. Each company has an equal chance of being awarded the
contract. If ESCO has already spent $100,000 in developing its
bidding proposal, what is its expected net profit?
A.$100,000
B.$90,000
C.-$10,000
D.$0
E(X) = (1/9) $900,000 = $100,000. ESCO only can expect to cover
its sunk cost (no profit).
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
55.The discrete random variable X is the number of students that
show up for Professor Smith's office hours on Monday afternoons.
The table below shows the probability distribution for X. What is
the expected value E(X) for this distribution?
A.1.2
B.1.0
C.1.5
D.2.0
For each X, multiply X time P(X) and sum the values.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
56.The discrete random variable X is the number of students that
show up for Professor Smith's office hours on Monday afternoons.
The table below shows the probability distribution for X. What is
the probability that at least 1 student comes to office hours on
any given Monday?
A..30
B..40
C..50
D..60
P(X 1) = 1 - P(X = 0) = 1 - .40 = .60.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
57.The discrete random variable X is the number of students that
show up for Professor Smith's office hours on Monday afternoons.
The table below shows the probability distribution for X. What is
the probability that fewer than 2 students come to office hours on
any given Monday?
A..10
B..40
C..70
D..90
P(X < 2) = P(X = 0) + P(X = 1) = .40 + .30 = .70.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
58.The discrete random variable X is the number of passengers
waiting at a bus stop. The table below shows the probability
distribution for X. What is the expected value E(X) for this
distribution?
A.1.1
B.1.3
C.1.7
D.1.9
For each X, multiply X time P(X) and sum the values.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
59.Given the following probability distribution, what is the
expected value of the random variable X?
A.175
B.150
C.200
D.205
For each X, multiply X time P(X) and sum the values.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-02 Solve problems using expected value and
variance.Topic: Discrete Distributions
60.Which of the following characterizes a Bernoulli process?
A.A random experiment that has only two outcomes.
B.The probability of "success" varies with each trial.
C.Either outcome has the same chance of occurrence.
D.The "success" must be a desirable outcome.
Review characteristics of the Bernoulli process.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Bernoulli Distribution
61.The binomial distribution describes the number of:
A.trials to obtain the first "success" in a Bernoulli
process.
B.trials to obtain n "successes" in a Bernoulli process.
C."successes" or "failures" in a Bernoulli process.
D."successes" in n Bernoulli trials.
Review characteristics of the binomial distribution.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
62.Which of the following is not a requirement of a binomial
distribution?
A.Constant probability of success
B.Only two possible Bernoulli outcomes
C.Fixed number of trials
D.Equally likely outcomes
Review characteristics of the binomial distribution.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
63.The binomial distribution is symmetrical when:
A. = 1 and 1 - = 0.
B. = and 1 - = .
C. = and 1 - = .
D. = 0 and 1 - = 1.
Review characteristics of the binomial distribution.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
64.The variance will reach a maximum in a binomial distribution
when:
A. = 1 and 1 - = 0.
B. = and 1 - = .
C. = and 1 - = .
D. = 0 and 1 - = 1.
Review formula for the binomial distribution standard
deviation.
AACSB: AnalyticBlooms: RememberDifficulty: 3 HardLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
65.Which distribution is most strongly right-skewed?
A.Binomial with n = 50, = .70
B.Binomial with n = 50, = .90
C.Binomial with n = 50, = .40
D.Binomial with n = 50, = .10
Review characteristics of the binomial distribution.
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
66.A random variable is binomially distributed with n = 16 and =
.40. The expected value and standard deviation of the variables
are:
A.2.00 and 1.24
B.4.80 and 4.00
C.6.40 and 1.96
D.2.00 and 1.20
Review characteristics of the binomial distribution.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
67.The expected value (mean) of a binomial variable is 15. The
number of trials is 20. The probability of "success" is:
A..25
B..50
C..75
D..30
Set E(X) = n = (20) = 15 and solve for .
AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
68.If 90 percent of automobiles in Orange County have both
headlights working, what is the probability that in a sample of
eight automobiles, at least seven will have both headlights
working?
A..6174
B..3826
C..8131
D..1869
Use Appendix A with n = 8 and = .90 to find P(X 7) or else use
the Excel function =1-BINOM.DIST(6,8,.90,1) = .8131.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
69.In Quebec, 90 percent of the population subscribes to the
Roman Catholic religion. In a random sample of eight Quebecois,
find the probability that the sample contains at least five Roman
Catholics.
A..0050
B..0331
C..9950
D..9619
Use Appendix A with n = 8 and = .90 to find P(X 5) or else use
the Excel function =1-BINOM.DIST(4,8,.90,1) = .99498.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
70.Hardluck Harry has a batting average of .200 (i.e., a 20
percent chance of a hit each time he's at bat). Scouts for a rival
baseball club secretly observe Harry's performance in 12 random
times at bat. What is the probability that Harry will get more than
2 hits?
A..2055
B..2362
C..7946
D..4417
Use Appendix A with n = 12 and = .20 to find P(X 3) or else use
the Excel function =1-BINOM.DIST(2,12,.20,1) = .44165.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
71.The probability that a visitor to an animal shelter will
adopt a dog is .20. Out of nine visits, what is the probability
that at least one dog will be adopted?
A..8658
B..3020
C..5639
D..1342
Use Appendix A with n = 9 and = .20 to find P(X 1) or else use
the Excel function =1-BINOM.DIST(0,9,.20,1) = .865778.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
72.Based on experience, 60 percent of the women who request a
pregnancy test at a certain clinic are actually pregnant. In a
random sample of 12 women, what is the probability that at least 10
are pregnant?
A..0639
B..1424
C..0196
D..0835
Use Appendix A with n = 12 and = .60 to find P(X 10) or else use
the Excel function =1-BINOM.DIST(9,12,.60,1) = .08344.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
73.If 5 percent of automobiles in Oakland County have one
burned-out headlight, what is the probability that, in a sample of
10 automobiles, none will have a burned-out headlight?
A..5987
B..3151
C..0116
D..1872
Use Appendix A with n = 10 and = .05 find P(X = 0) or else use
the Excel function =BINOM.DIST(0,10,.05,0) = .59874.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
74.Jankord Jewelers permits the return of their diamond wedding
rings, provided the return occurs within two weeks. Typically, 10
percent are returned. If eight rings are sold today, what is the
probability that fewer than three will be returned?
A..9950
B..9619
C..0331
D..1488
Use Appendix A with n = 8 and = .10 to find P(X < 3) or else
use the Excel function =BINOM.DIST(2,8,.1,1) = .96191.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
75.The probability that an Oxnard University student is carrying
a backpack is .70. If 10 students are observed at random, what is
the probability that fewer than 7 will be carrying backpacks?
A..3504
B..2001
C..6177
D..2668
Use Appendix A with n = 10 and = .70 to find P(X < 7) or else
use the Excel function =BINOM.DIST(6,10,.7,1) = .35039.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
76.An insurance company is issuing 16 car insurance policies.
Suppose the probability for a claim during a year is 15 percent. If
the binomial probability distribution is applicable, then the
probability that there will be at least two claims during the year
is equal to:
A..5615
B..2775
C..7161
D..0388
Use Appendix A with n = 16 and = .15 to find P(X 2) or else use
the Excel function =1-BINOM.DIST(1,16,.15,1) = .7161.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
77.A random variable X is distributed binomially with n = 8 and
= 0.70. The standard deviation of the variable X is
approximately:
A.0.458
B.2.828
C.1.680
D.1.296
Use the formula for the binomial standard deviation.
AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
78.Suppose X is binomially distributed with n = 12 and = .20.
The probability that X will be less than or equal to 3 is:
A..5584
B..7946
C..2362
D..7638
Use Appendix A with n = 12 and = .20 to find P(X 3) or else use
the Excel function =BINOM.DIST(3,12,.2,1) = .79457.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
79.Which Excel function would generate a single random X value
for a binomial random variable with parameters n = 16 and =
.25?
A.=BINOM.DIST(RAND(), 16, .25, 0)
B.=BINOM.DIST(0, 16, .25, RAND())
C.=BINOM.INV(16, .25, RAND())
D.=BINOM.INV(0, 16, .25, RAND())
This is the Excel 2010 function for the inverse of a
binomial.
AACSB: TechnologyBlooms: RememberDifficulty: 3 HardLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
80.A network has three independent file servers, each with 90
percent reliability. The probability that the network will be
functioning correctly (at least one server is working) at a given
time is:
A.99.9 percent.
B.97.2 percent.
C.95.9 percent.
D.72.9 percent.
Use Appendix A with n = 3 and = .90.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
81.Which statement concerning the binomial distribution is
correct?
A.Its PDF covers all integer values of X from 0 to n.
B.Its PDF is the same as its CDF when = .50.
C.Its CDF shows the probability of each value of X.
D.Its CDF is skewed right when < .50.
Review definitions of the binomial distribution. The binomial
domain is X = 0, 1, ..., n.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-03 Define probability distribution; PDF; and
CDF.Topic: Binomial Distribution
82.Historically, 2 percent of the stray dogs in Southfield are
unlicensed. On a randomly chosen day, the Southfield city animal
control officer picks up seven stray dogs. What is the probability
that fewer than two will be unlicensed?
A..8681
B..9921
C..3670
D..0076
Use Appendix A with n = 7 and = .02.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-05 Find binomial probabilities using tables;
formulas; or Excel.Topic: Binomial Distribution
83.The domain of X in a Poisson probability distribution is
discrete and can include:
A.any real X value.
B.any integer X value.
C.any nonnegative integer X value.
D.any X value except zero.
For a Poisson random variable, X = 0, 1, 2, (no upper
limit).
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
84.On Saturday morning, calls arrive at TicketMaster at a rate
of 108 calls per hour. What is the probability of fewer than three
calls in a randomly chosen minute?
A..1607
B..8913
C..2678
D..7306
Use Appendix B with = 108/60 = 1.8.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
85.On average, a major earthquake (Richter scale 6.0 or above)
occurs three times a decade in a certain California county. Find
the probability that at least one major earthquake will occur
within the next decade.
A..7408
B..1992
C..1494
D..9502
Use Appendix B with = 3.0.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
86.On average, an IRS auditor discovers 4.7 fraudulent income
tax returns per day. On a randomly chosen day, what is the
probability that she discovers fewer than two?
A..0518
B..0427
C..1005
D..1523
Use Appendix B with = 4.7.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
87.On a Sunday in April, dog bite victims arrive at Carver
Memorial Hospital at a historical rate of 0.6 victim per day. On a
given Sunday in April, what is the probability that exactly two dog
bite victims will arrive?
A..0875
B..0902
C..0988
D..0919
Use Appendix B with = 0.6.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
88.If tubing averages 16 defects per 100 meters, what is the
probability of finding exactly 2 defects in a randomly chosen
10-meter piece of tubing?
A..8795
B..2674
C..3422
D..2584
Use Appendix B with = 16/10 = 1.6.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
89.Cars are arriving at a toll booth at a rate of four per
minute. What is the probability that exactly eight cars will arrive
in the next two minutes?
A.0.0349
B.0.1396
C.0.9666
D.0.0005
Use Appendix B with = 4.0.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
90.Arrival of cars per minute at a toll booth may be
characterized by the Poisson distribution if:
A.the arrivals are independent.
B.no more than one arrival can occur in a minute.
C.there is only one lane leading to the booth.
D.the mean arrival rate is at least 30.
Events per unit of time with no clear upper limit.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
91.The coefficient of variation for a Poisson distribution with
= 5 is:
A.35.2 percent.
B.58.9 percent.
C.44.7 percent.
D.31.1 percent.
Use the coefficient of variation with standard deviation equal
to the square root of the mean.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
92.The coefficient of variation for a Poisson distribution with
= 4 is:
A.35.2 percent.
B.58.9 percent.
C.50.0 percent.
D.26.4 percent.
The Poisson standard deviation is the square root of the
mean.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-06 Find Poisson probabilities using tables; formulas;
or Excel.Topic: Poisson Distribution
93.For which binomial distribution would a Poisson approximation
be unacceptable?
A.n = 30, = 0.02
B.n = 50, = 0.03
C.n = 200, = 0.10
D.n = 500, = 0.01
We want n 20 and .05.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
94.For which binomial distribution would a Poisson approximation
be acceptable?
A.n = 60, = 0.08
B.n = 100, = 0.15
C.n = 40, = 0.03
D.n = 20, = 0.20
We want n 20 and .05 for an acceptable Poisson
approximation.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
95.For which binomial distribution would a Poisson approximation
not be acceptable?
A.n = 35, = 0.07
B.n = 95, = 0.01
C.n = 80, = 0.02
D.n = 50, = 0.03
We want n 20 and .05 for an acceptable Poisson
approximation.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
96.The true proportion of accounts receivable with some kind of
error is .02 for Venal Enterprises. If an auditor randomly samples
200 accounts receivable, what is the approximate Poisson
probability that fewer than two will contain errors?
A..1038
B..0916
C..1465
D..0015
Since n 20 and .05 we can set = n = (200)(.02) = 4.0 and use
Appendix B to find P(X 1), or else use the Excel cumulative
distribution function =POISSON.DIST(1,4.0,1) = .09158.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
97.The probability that a rental car will be stolen is 0.0004.
If 3500 cars are rented, what is the approximate Poisson
probability that 2 or fewer will be stolen?
A..3452
B..2417
C..5918
D..8335
Since n 20 and .05 we can set = n = (3500)(.0004) = 1.4 and use
Appendix B to find P(X 2), or else use the Excel cumulative
distribution function =POISSON.DIST(2,1.4,1) = .8335.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
98.The probability that a customer will use a stolen credit card
to make a purchase at a certain Target store is 0.003. If 400
purchases are made in a given day, what is the approximate Poisson
probability that 4 or fewer will be with stolen cards?
A..0053
B..0076
C..9923
D..0555
Since n 20 and .05 we can set = n = (400)(.003) = 1.2 and use
Appendix B, or else use the Excel cumulative distribution function
=POISSON.DIST(4,.003*400,1) = .9923.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
99.The probability that a ticket holder will miss a flight is
.005. If 180 passengers take the flight, what is the approximate
Poisson probability that at least 2 will miss the flight?
A..9372
B..0628
C..1647
D..2275
Since n 20 and .05 we can set = n = (.005)(180) = 0.9 and use
Appendix B to find P(X 2), or else use the Excel cumulative
distribution function = 1-POISSON.DIST(1,0.9,1) = .2275.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
100.The probability that a certain daily flight's departure from
ORD to LAX is delayed is .02. Over six months, this flight departs
180 times. What is the approximate Poisson probability that it will
be delayed fewer than 2 times?
A..4471
B..3028
C..1257
D..1771
Since n 20 and .05 we can set = n = (180)(.02) = 3.6 and use
Appendix B to find P(X 1) or else use the Excel cumulative
distribution function =POISSON.DIST(1,3.6,1) = .12569.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-07 Use the Poisson approximation to the binomial
(optional).Topic: Poisson Distribution
101.If X is a discrete uniform random variable ranging from 0 to
12, find P(X 10).
A..1126
B..1666
C..2308
D..2500
3 out of 13 outcomes (don't forget to count 0 as an
outcome).
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-04 Know the mean and variance of a uniform discrete
model.Topic: Uniform Distribution
102.If X is a discrete uniform random variable ranging from one
to eight, find P(X < 6).
A..6250
B..5000
C..7500
D..3750
We count five out of eight outcomes that meet this
requirement.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-04 Know the mean and variance of a uniform discrete
model.Topic: Uniform Distribution
103.If X is a discrete uniform random variable ranging from one
to eight, its mean is:
A.4.0
B.4.5
C.5.0
D.5.5
The mean is halfway between the lower and upper limits 1 and
8.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-04 Know the mean and variance of a uniform discrete
model.Topic: Uniform Distribution
104.If X is a discrete uniform random variable ranging from 12
to 24, its mean is:
A.18.5.
B.16.0.
C.18.0.
D.19.5.
The mean is halfway between the lower and upper limits 12 and
24.
AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning
Objective: 06-04 Know the mean and variance of a uniform discrete
model.Topic: Uniform Distribution
105.At Ersatz University, the graduating class of 480 includes
96 guest students from Latvia. A sample of 10 students is selected
at random to attend a dinner with the Board of Governors. Use the
binomial model to obtain the approximate hypergeometric probability
that the sample contains at least three Latvian students.
A..3222
B..1209
C..8791
D..6778
Since n/N < .05 we can use Appendix A with n = 10 and =
96/480 = .20 to find P(X 3).
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
106.There are 90 passengers on a commuter flight from SFO to
LAX, of whom 27 are traveling on business. In a random sample of
five passengers, use the binomial model to find the approximate
hypergeometric probability that there is at least one business
passenger.
A..3087
B..1681
C..3602
D..8319
Since n/N < .05 we can use Appendix A with n = 5 and = 27/90
= .30 to find P(X 1).
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
107.Use the binomial model to find the approximate
hypergeometric probability of at least two damaged flash drives in
a sample of five taken from a shipment of 150 that contains 30
damaged flash drives.
A.0.9421
B.0.0579
C.0.7373
D.0.2627
Since n/N < .05 we can use Appendix A with n = 5 and = 30/150
= .20 to find P(X 2).
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
108.On a particular day, 112 of 280 passengers on a particular
DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding
passes. In a random sample of eight passengers, use the binomial
model to find the approximate hypergeometric probability that four
will have used the e-ticket check-in kiosk to obtain boarding
passes.
A..2322
B..8263
C..2926
D..5613
Since n/N < .05 we can use Appendix A with n = 8 and =
112/280 = .40 to find P(X = 4).
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
109.A clinic employs nine physicians. Five of the physicians are
female. Four patients arrive at once. Assuming the doctors are
assigned randomly to patients, what is the probability that all of
the assigned physicians are female?
A..0397
B..0295
C..0808
D..0533
You can't use the binomial approximation because we have sampled
more than 5% of the population (n/N = 4/9 = .444) so use the
hypergeometric formula with x = 4, n = 4, s = 5, N = 9 or use the
Excel function =HYPGEOM.DIST(4,4,5,9,0) = .03938.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-08 Find hypergeometric probabilities using
Excel.Topic: Hypergeometric Distribution
110.There is a .02 probability that a customer's Visa charge
will be rejected at a certain Target store because the transaction
exceeds the customer's credit limit. What is the probability that
the first such rejection occurs on the third Visa transaction?
A..0192
B..0025
C..0247
D..0200
Use the formulas for the geometric PDF (not the CDF) with = .02
to find P(X = 3) = .02(1 - .02)3-1 = .02(.98)2 = .02(.9604) =
.019208.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
111.Ten percent of the corporate managers at Axolotl Industries
majored in humanities. What is the probability that the first
humanities major is the fifth manager you meet?
A..0656
B..8561
C..5904
D..4095
Use the formulas for the geometric PDF (not the CDF) with = .10
to find P(X = 5) = .10(1 - .10)5-1 = .10(.90)4 = .10(.6561) =
.06561.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
112.Ten percent of the corporate managers at Axolotl Industries
majored in humanities. What is the expected number of managers to
be interviewed until finding the first one with a humanities
major?
A.15
B.20
C.10
D.17
The geometric mean is 1/ = 1/(.10) = 10.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
113.When you send out a resume, the probability of being called
for an interview is .20. What is the probability that the first
interview occurs on the fourth resume that you send out?
A..4096
B..1024
C..2410
D..0016
Use the formulas for the geometric PDF (not the CDF) with = .20
to find P(X = 4) = .20(1 - .20)4-1 = .20(.80)3 = .20(.512) =
.1024.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
114.When you send out a resume, the probability of being called
for an interview is .20. What is the expected number of resumes you
send out until you get the first interview?
A.5
B.7
C.10
D.12
The geometric mean is 1/ = 1/(.20) = 5.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
115.When you send out a resume, the probability of being called
for an interview is .20. What is the probability that you get your
first interview within the first five resumes that you send
out?
A..6723
B..1024
C..2410
D..0016
Use the formulas for the geometric CDF (not the PDF) with = .20
to find P(X 5) = 1 -(1-.20)5 = = 1 - (.80)5 = 1 - .32678 =
.67232.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
116.There is a .02 probability that a customer's Visa charge
will be rejected at a certain Target store because the transaction
exceeds the customer's credit limit. What is the probability that
the first such rejection occurs within the first 20 Visa
transactions?
A..1362
B..4000
C..3324
D..4538
Use the formulas for the geometric CDF (not the PDF) with = .02
to find P(X 20) = 1 -(1-.02)20 = = 1 - (.98)20 = 1 - .6676 =
.3324.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
117.There is a .02 probability that a customer's Visa charge
will be rejected at a certain Target store because the transaction
exceeds the customer's credit limit. What is the expected number of
Visa transactions until the first one is rejected?
A.10
B.20
C.50
D.98
The geometric mean is 1/ = 1/(.02) = 50.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
118.The geometric distribution best describes:
A.the number of successes in a sample of n trials.
B.the number of trials until the first success.
C.the number of events in a given unit of time.
D.the process of sampling without replacement.
Review the definition of geometric distribution.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
119.The CDF for the geometric distribution shows:
A.the probability of success in a random experiment consisting
of n independent trials.
B.the probability that the first success will occur within a
given number of trials.
C.the probability that no success will be obtained in a given
Bernoulli trial.
D.the probability of more than one success in the first n
trials.
Review the definition of geometric distribution.
AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
120.If the probability of success is .25, what is the
probability of obtaining the first success within the first three
trials?
A..4218
B..5781
C..1406
D..2228
Use the formulas for the geometric CDF (not the PDF) with = .25
to find P(X 3) = 1 -(1-.25)3 = 1 - (.75)3 = 1 - .421875 =
.578125.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
121.If the probability of success is .30, what is the
probability of obtaining the first success within the first five
trials?
A..0024
B..8319
C..1681
D..9976
Use the formulas for the geometric CDF (not the PDF) with = .30
to find P(X 5) = 1 -(1-.30)5 = 1 - (.70)5 = 1 - .16807 =
.83193.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-09 Calculate geometric probabilities
(optional).Topic: Geometric Distribution (Optional)
122.A project has three independent stages that must be
completed in sequence. The time to complete each stage is a random
variable. The expected times to complete the stages are 1 = 23, 2 =
11, 3 = 17. The expected project completion time is:
A.51.
B.23.
C.40.
D.32.
The means can be summed because the stages are independent.
AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning
Objective: 06-11 Apply rules for transformations of random
variables (optional).Topic: Transformations of Random Variables
(Optional)
123.A project has 3 independent stages that must be completed in
sequence. The time to complete each stage is a random variable. The
standard deviations of the completion times for the stages are 1 =
5, 2 = 4, 3 = 6. The standard deviation of the overall project
completion time is:
A.8.77
B.15.0
C.14.2
D.9.24
The variances can be summed because the stages are independent
(Rule 4). You have to square the standard deviations to get the
variances 12 = 25, 22 = 16, 32 = 36, then add them and take the
square root of the sum. Be careful - the standard deviations cannot
be summed.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-11 Apply rules for transformations of random
variables (optional).Topic: Transformations of Random Variables
(Optional)
124.A stock portfolio consists of two stocks X and Y. Their
daily closing prices are independent random variables with standard
deviations X = 2.51 and Y = 5.22. What is the standard deviation of
the sum of the closing prices of these two stocks?
A.33.55
B.6.48
C.7.73
D.5.79
The variances can be summed because the stages are independent
(Rule 4). You have to square the standard deviations to get the
variances X2 = 6.3001 and Y2 = 27.2484, then add them and take the
square root of the sum. Be careful - the standard deviations cannot
be summed.
AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning
Objective: 06-11 Apply rules for transformations of random
variables (optional).Topic: Transformations of Random Variables
(Optional)
125.A stock portfolio consists of two stocks X and Y. Their
daily closing prices are correlated random variables with variances
X2 = 3.51 and Y2 = 5.22, and covariance XY = -1.55. What is the
standard deviation of the sum of the closing prices of these two
stocks?
A.5.63
B.7.18
C.8.73
D.2.68
Use the formula for the variance of correlated (nonindependent)
events. We sum the variances and covariance, and then take the
square root: X+Y = [X2 + Y2 + XY ]1/2 = [3.51 + 5.22 - 1.55]1/2 =
[7.18]1/2 = 2.67955.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-11 Apply rules for transformations of random
variables (optional).Topic: Transformations of Random Variables
(Optional)
126.The expected value of a random variable X is 140 and the
standard deviation is 14. The standard deviation of the random
variable Y = 3X - 10 is:
A.42
B.6.48
C.14
D.32
Use the rule for functions of a random variable (Rule 2) to get
Y = 3X = (3)(14) = 42. The constant -10 merely shifts the
distribution and has no effect on the standard deviation. The mean
of Y is not requested.
AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning
Objective: 06-11 Apply rules for transformations of random
variables (optional).Topic: Transformations of Random Variables
(Optional)
127.The expected value of a random variable X is 10 and the
standard deviation is 2. The standard deviation of the random
variable Y = 2X - 10 is:
A.2
B.4
C.-10
D.-6
Use the rule for functions of a random variable (Rule 2) to get
Y = 2X = (2)(2) = 4. The constant -10 merely shifts the
distribution and has no effect on the standard deviation. The mean
of Y is not