Deck 5: Discrete Probability Distributions

Question 1

The expected value of a random variable X can be referred to as the population mean.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

The average temperature in Tampa,Florida,during a month of July

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

A discrete random variable X may assume an (infinitely)uncountable number of distinct values.

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

A continuous random variable X assumes an (infinitely)uncountable number of distinct values.

Question 16

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.

Question 17

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.

Question 18

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.

Question 19

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

Question 20

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

Question 21

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

Question 22

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

Question 23

What are the two key properties of a discrete probability distribution?

A) and
B) and
C) and
D)

Question 24

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%

Question 25

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

Question 26

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

Question 27

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

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

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

Question 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

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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.

Question 57

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

Question 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 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

Question 59

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.

Question 60

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

Question 61

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

Question 62

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

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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

Question 70

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

Question 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

Question 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 five or more of his free throws?

A)0.3632
B)0.5105
C)0.8737
D)0.8940

Question 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 standard deviation of the number of free throws that Billups will make?

A)0.5364
B)0.5686
C)0.7540
D)5.6860

Question 74

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

Question 75

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

Question 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.

Question 77

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

Question 78

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

Question 79

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

Question 80

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