Deck 5: Discrete Probability Distributions

Question 1

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.

Answer 1

False

Question 2

The ounces of soda consumed by an adult next month are an example of a discrete random variable.

Answer 2

False

Question 3

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

Answer 3

False

Question 4

The equation used to calculate binomial probabilities relies on permutations of n objects selected x at a time.

Question 5

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

Question 6

The number of syntactic errors found in a program code would best be described using a Poisson probability distribution.

Question 7

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

Question 8

Testing whether the computer is infected or not would be best described using binomial probability distribution.

Question 9

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 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 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.

Question 16

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

Question 17

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

Question 18

The expected value of simple information is the mean of a discrete probability distribution when the discrete random variable is expressed in term of dollars.

Question 19

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

Question 20

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

Question 21

An Excel's function _________ is used for calculating Poisson probabilities.

Question 22

The risk of the portfolio depends not only on the individual risks of the assets but also on the ________ between the asset returns.

Question 23

A risk-averse consumer demands a(n)_______ expected gain as compensation for taking risk.

Question 24

Which of the following can be represented by a continuous random variable?

A) The average temperature in Tampa,Florida,during the 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 a.m.and 11:00 a.m.on Mondays

Question 25

Consider the following discrete probability distribution. What is the probability that X is negative?

A) 0.00
B) 0.10
C) 0.15
D) 0.35

Question 26

What is a characteristic of the mass function of a discrete random variable X?

A) The sum of probabilities P(X =x)over all possible values x is 1.
B) For every possible value x,the probability P(X =x)is between 0 and 1.
C) Describes all possible values x with the associated probabilities P(X =x).
D) All the above.

Question 27

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

A) 0≤P(X = x)≤1 and ∑P (X = x_i )= 0
B) 0≤P(X = x)≤1 and ∑P (X = x_i )= 1
C) -1≤P(X = x)≤1 and ∑P (X = x_i )= 1
D) -1≤P(X = x)≤1 and ∑P (X = x_i )= 0

Question 28

Consider the following discrete probability distribution. What is the probability that X is 0?

A) 0.10
B) 0.35
C) 0.55
D) 0.65

Question 29

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 30

To illustrate the possible outcomes and their associated probabilities we can construct a probability ______.

Question 31

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 32

Consider the following cumulative distribution function for the discrete random variable X. What is the probability that X is greater than 2?

A) 0.14
B) 0.30
C) 0.44
D) 0.56

Question 33

The Excel's function HYPERGEOM.DIST can be used to solve hypergeometric probabilities.

Question 34

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 five
C) The number of arrivals to a drive-through bank window in a four-hour period
D) The score of a randomly selected student on a five-question multiple-choice quiz

Question 35

Consider the following cumulative distribution function for the discrete random variable. What is the probability that X equals 2?

A) 0.14
B) 0.30
C) 0.44
D) 0.56

Question 36

The hypergeometric probability distribution is appropriate in applications where we cannot assume the trials are _________.

Question 37

Consider the following cumulative distribution function for the discrete random variable. 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 38

The following formula defines the ________ of a hypergeometric random variable

Question 39

Consider the following discrete probability distribution. What is the probability that X is greater than 0?

A) 0.10
B) 0.35
C) 0.55
D) 0.65

Question 40

Consider the following discrete probability distribution. What is the probability that X is less than 5?

A) 0.10
B) 0.15
C) 0.35
D) 0.45

Question 41

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the probability that the salesperson will sell one car during a week?

A) 0.20
B) 0.40
C) 0.60
D) 0.80

Question 42

Consider the following probability distribution. The variance is _____.

A) 1.14
B) 1.29
C) 1.65
D) 1.94

Question 43

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 44

The number of homes sold by a realtor during a month has the following probability distribution: 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 45

Consider the following probability distribution. The expected value is _____.

A) -1.0
B) -0.1
C) 0.1
D) 1.0

Question 46

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the standard deviation of the number of cars sold by the salesperson during a week?

A) 0.56
B) 0.75
C) 0.80
D) 1

Question 47

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 48

The number of homes sold by a realtor during a month has the following probability distribution: 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 49

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 or her decisions based solely on expected values
D) None of the above

Question 50

Consider the following probability distribution. The variance is ____.

A) 0.89
B) 0.94
C) 1.65
D) 1.90

Question 51

The number of homes sold by a realtor during a month has the following probability distribution: 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 52

Consider the following probability distribution. The standard deviation is ____.

A) 1.14
B) 1.29
C) 1.65
D) 1.94

Question 53

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 _____ and _____. Expected Value Variance

A) 1 4.58
B) 2 21.00
C) 2.5 4.58
D) 2.5 21.00

Question 54

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the expected number of cars sold by the salesperson during a week?

A) 0
B) 0.8
C) 1
D) 1.5

Question 55

Consider the following probability distribution. The expected value is _____.

A) 0.9
B) 1.5
C) 1.9
D) 2.5

Question 56

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 or her decisions based solely on expected values
D) None of the above

Question 57

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 1,000 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 58

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the probability that the salesperson sells no more than one car during a week?

A) 0.20
B) 0.40
C) 0.60
D) 0.80

Question 59

The number of homes sold by a realtor during a month has the following probability distribution: 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 60

Consider the following probability distribution. The standard deviation is _________.

A) 0.89
B) 0.94
C) 1.65
D) 1.90

Question 61

According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011.Eight working-age residents were chosen at random.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 62

According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011.Eight working-age residents were chosen at random.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 63

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 64

On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected.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 65

According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries.Suppose seven expectant mothers are randomly selected.What is the probability that at least one of the expectant mothers will have a Caesarean delivery?

A) 0.0606
B) 0.2090
C) 0.9394
D) 0.9742

Question 66

On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected.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 67

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 68

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.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 69

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.What is the expected number of coupons that will be redeemed?

A) 0.81
B) 0.96
C) 3.42
D) 5.04

Question 70

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 71

On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected.What is the probability that two light bulbs will be defective?

A) 0.0105
B) 0.0746
C) 0.3151
D) 0.5987

Question 72

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 or her decisions solely on the basis of expected values.
D) None of the above.

Question 73

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 74

According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries.Suppose seven expectant mothers are randomly selected.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 75

According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries.Suppose seven expectant mothers are randomly selected.What is the probability that two of the expectant mothers will have a Caesarean delivery?

A) 0.0147
B) 0.0606
C) 0.2090
D) 0.3088

Question 76

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.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 77

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 78

Which of the following statements is the 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 79

According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries.Suppose seven expectant mothers are randomly selected.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 80

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.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