# Quiz 5: Discrete Probability Distributions

Statistics

Q 1Q 1

A random variable is a function that assigns numerical values to the outcomes of a random experiment.

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True False

True

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True False

False

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True False

True

Q 4Q 4

A probability distribution of a continuous random variable X gives the probability that X takes on a particular value x,P(X = x).

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True False

Q 5Q 5

A cumulative probability distribution of a random variable X is the probability P(X = x),where X is equal to a particular value x.

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True False

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True False

Q 7Q 7

The variance of a random variable X provides us with a measure of central location of the distribution of X.

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True False

Q 8Q 8

The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance.

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True False

Q 9Q 9

A risk-averse consumer may decline a risky prospect even if it offers a positive expected value.

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True False

Q 10Q 10

A risk averse consumer ignores risk and makes his/her decisions solely on the basis of expected value.

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True False

Q 11Q 11

Given two random variables X and Y,the expected value of their sum, ,is equal to the sum of their individual expected values, .

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True False

Q 12Q 12

A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

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True False

Q 13Q 13

A binomial random variable is defined as the number of successes achieved in n trials of a Bernoulli process.

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True False

Q 14Q 14

A Poisson random variable counts the number of successes (occurrences of a certain event)over a given interval of time or space.

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True False

Q 15Q 15

We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size N is significantly larger than the sample size n.

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True False

Q 16Q 16

Which of the following can be represented by a discrete random variable?
A)The number of obtained spots when rolling a six-sided die
B)The height of college students
C)The average outside temperature taken every day for two weeks
D)The finishing time of participants in a cross-country meet

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Multiple Choice

Q 17Q 17

Which of the following can be represented by a discrete random variable?
A)The circumference of a randomly generated circle
B)The time of a flight between Chicago and New York
C)The number of defective light bulbs in a sample of five
D)The average distance achieved in a series of long jumps

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Multiple Choice

Q 18Q 18

Which of the following can be represented by a continuous random variable?
A)The time of a flight between Chicago and New York
B)The number of defective light bulbs in a sample of 5
C)The number of arrivals to a drive-thru bank window in a four-hour period
D)The score of a randomly selected student on a five-question multiple-choice quiz

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Multiple Choice

Q 19Q 19

Which of the following can be represented by a continuous random variable?
A)The average temperature in Tampa,Florida,during a month of July
B)The number of typos found on a randomly selected page of this test bank
C)The number of students who will get financial assistance in a group of 50 randomly selected students
D)The number of customers who visit a department store between 10:00 am and 11:00 am on Mondays

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Multiple Choice

Q 20Q 20

What is a characteristic of the mass function of a discrete random variable X?
A)The sum of probabilities over all possible values x is 1.
B)For every possible value x,the probability is between 0 and 1.
C)Describes all possible values x with the associated probabilities .
D)All of the above.

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Multiple Choice

Q 21Q 21

What are the two key properties of a discrete probability distribution?
A) and
B) and
C) and
D)

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Multiple Choice

Q 22Q 22

Exhibit 5-1.Consider the following discrete probability distribution. Refer to Exhibit 5-1.What is the probability that X is 0?
A)0.10
B)0.35
C)0.55
D)0.65

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Multiple Choice

Q 23Q 23

Exhibit 5-1.Consider the following discrete probability distribution. Refer to Exhibit 5-1.What is the probability that X is greater than 0?
A)0.10
B)0.35
C)0.55
D)0.65

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Multiple Choice

Q 24Q 24

Exhibit 5-1.Consider the following discrete probability distribution. Refer to Exhibit 5-1.What is the probability that X is negative?
A)0.00
B)0.10
C)0.15
D)0.35

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Multiple Choice

Q 25Q 25

Exhibit 5-1.Consider the following discrete probability distribution. Refer to Exhibit 5-1.What is the probability that X is less than 5?
A)0.10
B)0.15
C)0.35
D)0.45

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Multiple Choice

Q 26Q 26

Exhibit 5-2.Consider the following cumulative distribution function for the discrete random variable X. Refer to Exhibit 5-2.What is the probability that X is less than or equal to 2?
A)0.14
B)0.30
C)0.44
D)0.56

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Multiple Choice

Q 27Q 27

Exhibit 5-2.Consider the following cumulative distribution function for the discrete random variable X. Refer to Exhibit 5-2.What is the probability that X equals 2?
A)0.14
B)0.30
C)0.44
D)0.56

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Multiple Choice

Q 28Q 28

Exhibit 5-2.Consider the following cumulative distribution function for the discrete random variable X. Refer to Exhibit 5-2.What is the probability that X is greater than 2?
A)0.14
B)0.30
C)0.44
D)0.56

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Multiple Choice

Q 29Q 29

We can think of the expected value of a random variable X as ________________.
A)The long-run average of the random variable values generated over 100 independent repetitions
B)The long-run average of the random variable values generated over 1000 independent repetitions
C)The long-run average of the random variable values generated over infinitely many independent repetitions
D)The long-run average of the random variable values generated over a finite number of independent repetitions

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Multiple Choice

Q 30Q 30

The expected value of a random variable X can be referred to or denoted as _____.
A)µ
B)E(X)
C)The population mean
D)All of the above

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Multiple Choice

Q 31Q 31

Exhibit 5-3.Consider the following probability distribution. Refer to Exhibit 5-3.The expected value is ___.
A)0.9
B)1.5
C)1.9
D)2.5

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Multiple Choice

Q 32Q 32

Exhibit 5-3.Consider the following probability distribution. Refer to Exhibit 5-3.The variance is ____.
A)0.89
B)0.94
C)1.65
D)1.90

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Multiple Choice

Q 33Q 33

Exhibit 5-3.Consider the following probability distribution. Refer to Exhibit 5-3.The standard deviation is _________.
A)0.89
B)0.94
C)1.65
D)1.90

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Multiple Choice

Q 34Q 34

Exhibit 5-4.Consider the following probability distribution. Refer to Exhibit 5-4.The expected value is _____.
A)-1.0
B)-0.1
C)0.1
D)1.0

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Multiple Choice

Q 35Q 35

Exhibit 5-4.Consider the following probability distribution. Refer to Exhibit 5-4.The variance is _____.
A)1.14
B)1.29
C)1.65
D)1.94

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Multiple Choice

Q 36Q 36

Exhibit 5-4.Consider the following probability distribution. Refer to Exhibit 5-4.The standard deviation is ____.
A)1.14
B)1.29
C)1.65
D)1.94

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Multiple Choice

Q 37Q 37

An analyst has constructed the following probability distribution for firm X's predicted return for the upcoming year. The expected value and the variance of this distribution are:
A)Option A
B)Option B
C)Option C
D)Option D

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Multiple Choice

Q 38Q 38

An analyst believes that a stock's return depends on the state of the economy,for which she has estimated the following probabilities: According to the analyst's estimates,the expected return of the stock is ____.
A)7.8%
B)11.4%
C)11.7%
D)13.0%

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Multiple Choice

Q 39Q 39

An analyst estimates that the year-end price of a stock has the following probabilities: The stock's expected price at the end of the year is _______.
A)$87.50
B)$88.50
C)$89.00
D)$90.00

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Multiple Choice

Q 40Q 40

Exhibit 5-5.The number of homes sold by a realtor during a month has the following probability distribution: Refer to Exhibit 5-5.What is the probability that the realtor will sell at least one house during a month?
A)0.20
B)0.40
C)0.60
D)0.80

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Multiple Choice

Q 41Q 41

Exhibit 5-5.The number of homes sold by a realtor during a month has the following probability distribution: Refer to Exhibit 5-5.What is the probability that the realtor sells no more than one house during a month?
A)0.20
B)0.40
C)0.60
D)0.80

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Multiple Choice

Q 42Q 42

Exhibit 5-5.The number of homes sold by a realtor during a month has the following probability distribution: Refer to Exhibit 5-5.What is the expected number of homes sold by the realtor during a month?
A)1
B)1.2
C)1.5
D)2

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Multiple Choice

Q 43Q 43

Exhibit 5-5.The number of homes sold by a realtor during a month has the following probability distribution: Refer to Exhibit 5-5.What is the standard deviation of the number of homes sold by the realtor during a month?
A)0.56
B)0.75
C)1
D)1.2

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Multiple Choice

Q 44Q 44

Exhibit 5-6.The number of cars sold by a car salesman during each of the last 25 weeks is the following: Refer to Exhibit 5-6.What is the probability that the salesman will sell one car during a week?
A)0.20
B)0.40
C)0.60
D)0.80

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Multiple Choice

Q 45Q 45

Exhibit 5-6.The number of cars sold by a car salesman during each of the last 25 weeks is the following: Refer to Exhibit 5-6.What is the probability that the salesman sells no more than one car during a week?
A)0.20
B)0.40
C)0.60
D)0.80

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Multiple Choice

Q 46Q 46

Exhibit 5-6.The number of cars sold by a car salesman during each of the last 25 weeks is the following: Refer to Exhibit 5-6.What is the expected number of cars sold by the salesman during a week?
A)0
B)0.8
C)1
D)1.5

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Multiple Choice

Q 47Q 47

Exhibit 5-6.The number of cars sold by a car salesman during each of the last 25 weeks is the following: Refer to Exhibit 5-6.What is the standard deviation of the number of cars sold by the salesman during a week?
A)0.56
B)0.75
C)0.80
D)1

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Multiple Choice

Q 48Q 48

A consumer who is risk averse is best characterized as _______________.
A)A consumer who may accept a risky prospect even if the expected gain is negative
B)A consumer who demands a positive expected gain as compensation for taking risk
C)A consumer who completely ignores risk and makes his/her decisions based solely on expected values
D)None of the above

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Multiple Choice

Q 49Q 49

A consumer who is risk neutral is best characterized as ______________.
A)A consumer who may accept a risky prospect even if the expected gain is negative
B)A consumer who demands a positive expected gain as compensation for taking risk
C)A consumer who completely ignores risk and makes his/her decisions based solely on expected values
D)None of the above

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Multiple Choice

Q 50Q 50

How would you characterize a consumer who is risk loving?
A)A consumer who may accept a risky prospect even if the expected gain is negative.
B)A consumer who demands a positive expected gain as compensation for taking risk.
C)A consumer who completely ignores risk and makes his/her decisions solely on the basis of expected values.
D)None of the above.

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Multiple Choice

Q 51Q 51

Which of the following statements is most accurate about a binomial random variable?
A)It has a bell-shaped distribution.
B)It is a continuous random variable.
C)It counts the number of successes in a given number of trials.
D)It counts the number of successes in a specified time interval or region.

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Multiple Choice

Q 52Q 52

It is known that 10% of the calculators shipped from a particular factory are defective.What is the probability that exactly three of five chosen calculators are defective?
A)0.00729
B)0.0081
C)0.081
D)0.03

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Multiple Choice

Q 53Q 53

It is known that 10% of the calculators shipped from a particular factory are defective.What is the probability that none in a random sample of four calculators is defective?
A)0.0010
B)0.2916
C)0.3439
D)0.6561

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Multiple Choice

Q 54Q 54

It is known that 10% of the calculators shipped from a particular factory are defective.What is the probability that at least one in a random sample of four calculators is defective?
A)0.0010
B)0.2916
C)0.3439
D)0.6561

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Multiple Choice

Q 55Q 55

Thirty percent of the CFA candidates have a degree in economics.A random sample of three CFA candidates is selected.What is the probability that none of them has a degree in economics?
A)0.027
B)0.300
C)0.343
D)0.900

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Multiple Choice

Q 56Q 56

Thirty percent of the CFA candidates have a degree in economics.A random sample of three CFA candidates is selected.What is the probability that at least one of them has a degree in economics?
A)0.300
B)0.343
C)0.657
D)0.900

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Multiple Choice

Q 57Q 57

Exhibit 5-9.On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected. Refer to Exhibit 5-9.What is the probability that two light bulbs will be defective?
A)0.0105
B)0.0746
C)0.3151
D)0.5987

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Multiple Choice

Q 58Q 58

Exhibit 5-9.On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected. Refer to Exhibit 5-9.What is the probability that none of the light bulbs will be defective?
A)0.0105
B)0.0746
C)0.3151
D)0.5987

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Multiple Choice

Q 59Q 59

Exhibit 5-9.On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected. Refer to Exhibit 5-9.What are the mean and variance of the number of defective bulbs?
A)0.475 and 0.475
B)0.475 and 0.6892
C)0.50 and 0.475
D)0.50 and 0.6892

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Multiple Choice

Q 60Q 60

Exhibit 5-10.According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries (National Vital Statistics Report,Volume 60,Number 2,November 2011).Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10.What is the probability that 2 of the expectant mothers will have a Caesarean delivery?
A)0.0147
B)0.0606
C)0.2090
D)0.3088

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Multiple Choice

Q 61Q 61

Exhibit 5-10.According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries (National Vital Statistics Report,Volume 60,Number 2,November 2011).Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10.What is the probability that at least 1 of the expectant mothers will have a Caesarean delivery?
A)0.0606
B)0.2090
C)0.9394
D)0.9742

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Multiple Choice

Q 62Q 62

Exhibit 5-10.According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries (National Vital Statistics Report,Volume 60,Number 2,November 2011).Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10.The expected number of mothers who will not have a Caesarean delivery is ______.
A)1.24
B)2.31
C)3.50
D)4.69

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Multiple Choice

Q 63Q 63

Exhibit 5-10.According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries (National Vital Statistics Report,Volume 60,Number 2,November 2011).Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10.What is the standard deviation of the number of mothers who will have a Caesarean delivery?
A)1.24
B)1.54
C)2.31
D)4.69

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Multiple Choice

Q 64Q 64

Exhibit 5-11.For a particular clothing store,a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed.Suppose six customers are randomly selected and are mailed $10-off coupons. Refer to Exhibit 5-11.What is the probability that three of the customers redeem the coupon?
A)0.0486
B)0.1912
C)0.3513
D)0.4015

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Multiple Choice

Q 65Q 65

Exhibit 5-11.For a particular clothing store,a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed.Suppose six customers are randomly selected and are mailed $10-off coupons. Refer to Exhibit 5-11.What is the probability that no more than one of the customers redeems the coupon?
A)0.2472
B)0.3513
C)0.4015
D)0.7528

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Multiple Choice

Q 66Q 66

Exhibit 5-11.For a particular clothing store,a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed.Suppose six customers are randomly selected and are mailed $10-off coupons. Refer to Exhibit 5-11.What is the probability that at least two of the customers redeem the coupon?
A)0.2472
B)0.3513
C)0.4015
D)0.7528

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Multiple Choice

Q 67Q 67

Exhibit 5-11.For a particular clothing store,a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed.Suppose six customers are randomly selected and are mailed $10-off coupons. Refer to Exhibit 5-11.What is the expected number of coupons that will be redeemed?
A)0.81
B)0.96
C)3.42
D)5.04

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Multiple Choice

Q 68Q 68

Exhibit 5-12.According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011 (Bureau of Labor Statistics,May,2011).Eight working-age residents were chosen at random. Refer to Exhibit 5-12.What is the probability that exactly one of the residents was unemployed?
A)0.0419
B)0.1678
C)0.2936
D)0.3355

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Multiple Choice

Q 69Q 69

Exhibit 5-12.According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011 (Bureau of Labor Statistics,May,2011).Eight working-age residents were chosen at random. Refer to Exhibit 5-12.What is the probability that at least two of the residents were unemployed?
A)0.1678
B)0.3355
C)0.4967
D)0.5033

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Multiple Choice

Q 70Q 70

Exhibit 5-12.According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011 (Bureau of Labor Statistics,May,2011).Eight working-age residents were chosen at random. Refer to Exhibit 5-12.What is the probability that exactly four residents were unemployed?
A)0.0013
B)0.0091
C)0.0459
D)0.1468

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Multiple Choice

Q 71Q 71

Exhibit 5-12.According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011 (Bureau of Labor Statistics,May,2011).Eight working-age residents were chosen at random. Refer to Exhibit 5-12.What was the expected number of unemployed residents,when eight working-age residents were randomly selected?
A)1.0
B)1.6
C)2.0
D)6.4

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Multiple Choice

Q 72Q 72

Exhibit 5-13.Chauncey Billups,a current shooting guard for the Los Angeles Clippers,has a career free-throw percentage of 89.4%.Suppose he shoots six free throws in tonight's game. Refer to Exhibit 5-13.What is the probability that Billups makes all six free throws?
A)0.1070
B)0.3632
C)0.5105
D)0.6530

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Multiple Choice

Q 73Q 73

Exhibit 5-13.Chauncey Billups,a current shooting guard for the Los Angeles Clippers,has a career free-throw percentage of 89.4%.Suppose he shoots six free throws in tonight's game. Refer to Exhibit 5-13.What is the probability that Billups makes five or more of his free throws?
A)0.3632
B)0.5105
C)0.8737
D)0.8940

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Multiple Choice

Q 74Q 74

Exhibit 5-13.Chauncey Billups,a current shooting guard for the Los Angeles Clippers,has a career free-throw percentage of 89.4%.Suppose he shoots six free throws in tonight's game. Refer to Exhibit 5-13.What is the expected number of free throws that Billups will make?
A)0.636
B)5.364
C)5.686
D)6.000

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Multiple Choice

Q 75Q 75

Exhibit 5-13.Chauncey Billups,a current shooting guard for the Los Angeles Clippers,has a career free-throw percentage of 89.4%.Suppose he shoots six free throws in tonight's game. Refer to Exhibit 5-13.What is the standard deviation of the number of free throws that Billups will make?
A)0.5364
B)0.5686
C)0.7540
D)5.6860

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Multiple Choice

Q 76Q 76

Which of the following statements is most accurate about a Poisson random variable?
A)It counts the number of successes in a given number of trials.
B)It counts the number of successes in a specified time or space interval.
C)It is a continuous random variable.
D)It has a bell-shaped distribution.

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Multiple Choice

Q 77Q 77

Exhibit 5-14.The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005. Refer to Exhibit 5-14.What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?
A)0.1680
B)0.1954
C)0.2240
D)0.8153

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Multiple Choice

Q 78Q 78

Exhibit 5-14.The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005. Refer to Exhibit 5-14.What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?
A)0.0498
B)0.1494
C)0.8009
D)0.9502

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Multiple Choice

Q 79Q 79

Exhibit 5-14.The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005. Refer to Exhibit 5-14.What is the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?
A)0.1991
B)0.2240
C)0.4232
D)0.5768

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Multiple Choice

Q 80Q 80

Exhibit 5-14.The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005. Refer to Exhibit 5-14.What is the probability that exactly 10 foreclosure auctions occurred during a randomly selected five-day week in 2011 in Boston?
A)0.0008
B)0.0486
C)0.1185
D)0.9514

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Multiple Choice

Q 81Q 81

Exhibit 5-15.A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson-distributed. Refer to Exhibit 5-15.What is the probability that exactly three customers enter the queue in a randomly selected five-minute period?
A)0.0902
B)0.1804
C)0.2240
D)0.2707

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Multiple Choice

Q 82Q 82

Exhibit 5-15.A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson-distributed. Refer to Exhibit 5-15.What is the probability that less than two customers enter the queue in a randomly selected five-minute period?
A)0.1353
B)0.2707
C)0.4060
D)0.6767

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Multiple Choice

Q 83Q 83

Exhibit 5-15.A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson-distributed. Refer to Exhibit 5-15.What is the probability that at least two customers enter the queue in a randomly selected five-minute period?
A)0.1353
B)0.2707
C)0.4060
D)0.5940

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Multiple Choice

Q 84Q 84

Exhibit 5-15.A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson-distributed. Refer to Exhibit 5-15.What is the probability that exactly seven customers enter the queue in a randomly selected 15-minute period?
A)0.0034
B)0.1033
C)0.1377
D)0.1606

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Multiple Choice

Q 85Q 85

Cars arrive randomly at a tollbooth at a rate of 20 cars per 10 minutes during rush hour.What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
A)0.0378
B)0.0500
C)0.1251
D)0.5000

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Multiple Choice

Q 86Q 86

A roll of steel is manufactured on a processing line.The anticipated number of defects in a 10-foot segment of this roll is two.What is the probability of no defects in 10 feet of steel?
A)0.0002
B)0.1353
C)0.1804
D)0.8647

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Multiple Choice

Q 87Q 87

Exhibit 5-16.According to geologists,the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16.What is the probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years?
A)0.0067
B)0.0337
C)0.1353
D)0.2707

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Multiple Choice

Q 88Q 88

Exhibit 5-16.According to geologists,the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16.What is the probability that more than two earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next 40 years?
A)0.1353
B)0.2706
C)0.3233
D)0.8754

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Multiple Choice

Q 89Q 89

Exhibit 5-16.According to geologists,the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16.What is the probability that one or more earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next year?
A)0.0488
B)0.1353
C)0.4878
D)0.9512

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Multiple Choice

Q 90Q 90

Exhibit 5-16.According to geologists,the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16.What is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?
A)1.414
B)2.000
C)2.236
D)5.000

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Multiple Choice

Q 91Q 91

Which of the following is true about the hypergeometric distribution?
A)The trials are independent and the probability of success may change from trial to trial.
B)The trials are independent and the probability of success does not change from trial to trial.
C)The trials are not independent and the probability of success may change from trial to trial.
D)The trials are not independent and the probability of success does not change from trial to trial.

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Multiple Choice

Q 92Q 92

An urn contains 12 balls,5 of which are red.The selection of a red ball is desired and is therefore considered to be a success.If a person draws three balls from the urn,what is the probability of two successes?
A)0.1591
B)0.3182
C)0.6810
D)0.8409

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Multiple Choice

Q 93Q 93

An urn contains 12 balls,5 of which are red.Selection of a red ball is desired and is therefore considered to be a success.If three balls are selected,what is the expected value of the distribution of the number of selected red balls?
A)0.4167
B)0.8333
C)0.5833
D)1.2500

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Multiple Choice

Q 94Q 94

Exhibit 5-17.Suppose a baseball team has 14 players on the roster who are not members of the pitching staff.Of those 14 players,assume that 3 have recently taken a performance-enhancing drug.Suppose the league decides to randomly test five members of the team. Refer to Exhibit 5-17.What is the probability that exactly two of the tested players are found to have taken a performance-enhancing drug?
A)0.2308
B)0.2473
C)0.4945
D)0.7692

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Multiple Choice

Q 95Q 95

Exhibit 5-17.Suppose a baseball team has 14 players on the roster who are not members of the pitching staff.Of those 14 players,assume that 3 have recently taken a performance-enhancing drug.Suppose the league decides to randomly test five members of the team. Refer to Exhibit 5-17.What is the probability that at least one of the tested players is found to have taken a performance-enhancing drug?
A)0.2308
B)0.2473
C)0.4945
D)0.7692

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Multiple Choice

Q 96Q 96

Exhibit 5-18.There are currently 18 pit bulls at the pound.Of the 18 pit bulls,four have attacked another dog in the last year.Joe,a member of the staff,randomly selects six of the pit bulls for his group. Refer to Exhibit 5-18.What is the probability that exactly one of the pit bulls in Joe's group attacked another dog last year?
A)0.1618
B)0.3235
C)0.4314
D)0.4853

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Multiple Choice

Q 97Q 97

Exhibit 5-18.There are currently 18 pit bulls at the pound.Of the 18 pit bulls,four have attacked another dog in the last year.Joe,a member of the staff,randomly selects six of the pit bulls for his group. Refer to Exhibit 5-18.What is the probability that at least one of the pit bulls in Joe's group attacked another dog last year?
A)0.1618
B)0.4314
C)0.5686
D)0.8382

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Multiple Choice

Q 98Q 98

A six-sided,unfair (weighted)die has the following probability distribution. Find the probability of rolling a 3 or less.

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Q 100Q 100

An analyst estimates that a stock has the following probabilities of year-end prices. a.Calculate the expected price at year-end.
b.Calculate the variance and the standard deviation.

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Q 101Q 101

You have inherited a lottery ticket that may be a $5,000 winner.You have a 35% chance of winning the $5,000 and a 65% chance of winning $0.You have an opportunity to sell the lottery for $1500.What should you do if are risk neutral?

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Q 102Q 102

You have inherited a lottery ticket worth $10,000.You have a 0.25 chance of winning the $10,000 and a 0.75 chance of winning $0.You have an opportunity to sell the lottery ticket for $2,500.What should you do if you are risk averse?

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Q 103Q 103

Suppose your firm is buying five new computers.The manufacturer offers a warranty to replace any computer that breaks down within three years.Suppose there is a 25% chance that any given computer breaks down within three years.
a.What is the probability that exactly one of the computers breaks down within five years?
b.What is the probability that at least one of the computers breaks down within five years?
c.Suppose the warranty for five computers costs $700,while a new computer costs $600.Is the warranty less expensive than the expected cost of replacing the broken computers?

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Q 104Q 104

Lisa is in a free-throw shooting contest where each contestant attempts 10 free throws.On average,Lisa makes 77% of the free throws she attempts.
a.What is the probability that she makes exactly eight free throws?
b.What is the probability she makes at least nine free throws?
c.What is the probability she makes less than nine free throws?
d.Lisa is competing against Bill to see who can make the most free throws in 10 attempts.Suppose Bill goes first and makes seven.Should we expect Lisa to make at least as many as Bill? Explain.

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Q 105Q 105

George buys six lottery tickets for $2 each.In addition to the grand prize,there is a 20% chance that each lottery ticket gives a prize of $4.Assume that these tickets are not grand prize winners.
a.What is the probability that the tickets pay out more than George spent on them?
b.What is the probability that none of the tickets are winners?
c.What is the probability that at least one of the tickets is a winner?

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Q 106Q 106

A car salesman has a 5% chance of landing a sale with a random customer on his lot.Suppose 10 people come on the lot today.
a.What is the probability that he sells exactly three cars today?
b.What is the probability he sells less than two cars today?
c.What is the expected number of cars he is going to sell today?

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Q 107Q 107

A company is going to release four quarterly reports this year.Suppose the company has a 32% chance of beating analyst expectations each quarter.
a.What is the probability that the company beats analyst expectations every quarter of this year?
b.What is the probability the company beats analyst expectations more than half the time this year?
c.What is the probability of the expected number of times the company will beat analyst expectations this year?

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Q 108Q 108

Assume that the mean success rate of a Poisson process is six successes per hour.
a.Find the expected number of successes in a 40-minute period.
b.Find the expected number of successes in a three-hour period.
c.Find the probability of at least two successes in a 30-minute period.

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Q 109Q 109

Sam is a trucker and believes that for every 60 miles he drives on the freeway in Indiana,there is an average of 2 state troopers checking his speed with a radar gun.
a.What is the probability that at least one trooper is checking his speed on a randomly selected 60-mile stretch?
b.What is the probability that exactly three troopers are checking his speed on a randomly selected 60-mile stretch?
c.Sam drives 240 miles a day.What is the average number of state troopers that check his speed on a given day?
d.Sam drives 240 miles a day.What is the probability that exactly five troopers check Sam's speed on a randomly selected day?

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Q 110Q 110

Due to turnover and promotion,a bank manager knows that,on average,she hires four new tellers per year.Suppose the number of tellers she hires is Poisson-distributed.
a.What is the probability that in a given year,the manager hires exactly five new tellers?
b.What is the average number of tellers the manager hires in a six-month period?
c.What is the probability that the manager hires at least one new teller in a given six-month period?

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Q 111Q 111

A telemarketer knows that,on average,he is able to make three sales in a 30-minute period.Suppose the number of sales he can make in a given time period is Poisson-distributed.
a.What is the probability that he makes exactly four sales in a 30-minute period?
b.What is the probability that he makes at least two sales in a 30-minute period?
c.What is the probability that he makes five sales in an hour-long period?

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Q 112Q 112

A construction company found that on average its workers get into four car accidents per week.
a.What is the probability of exactly six car accidents in a random week?
b.What is the probability that there are less than two car accidents in a random week?
c.What is the probability that there are exactly eight car accidents over the course of three weeks?

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Q 113Q 113

During an hour of class,a professor anticipates six questions on average.
a.What is the probability that in a given hour of class,exactly six questions are asked?
b.What is the expected number of questions asked in a 20-minute period?
c.What is the probability that no questions are asked over a 20-minute period?

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Q 114Q 114

A plane taking off from an airport in New York can expect to run into a flock of birds once out of every 1,250 take-offs.
a.What is the expected number of bird strikes for 10,000 take-offs?
b.What is the standard deviation of the number of bird strikes for 10,000 take-offs?
c.What is the probability of running into seven flocks of birds in 10,000 take-offs?

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Q 115Q 115

You are attending a baseball game with two family members when it is announced that four fans in your section (which holds 20 spectators total)will win a free autographed baseball.
a.What is the probability that at least one member in your family (including yourself)wins an autographed baseball?
b.What is the probability that exactly two members of your family win an autographed baseball?
c.What is the probability that all three of you win an autographed baseball?

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Q 116Q 116

Four of your students submitted an entry to a writing contest.There were a total of 24 entries submitted.Six of the entries will move on to the next round.
a.What is the probability that all four of your students will move on to the next round?
b.How many of your students are expected to move to the next round?
c.What is the probability that fewer of your students than expected make it to the next round than expected?

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Q 117Q 117

In a particular game of cards,success is measured by the number of aces drawn by each player.Eight cards are drawn by the first player.Given that the player is drawing from a full poker deck of 52 cards,find the probability that this player will draw two aces from the deck.

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Q 118Q 118

An urn is filled with three different colors of balls: red,blue,and white.There are three red balls,seven blue balls,and five white balls.If four balls are drawn,what is the probability of drawing two blue balls?

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