Deck 5: Discrete Random Variables and Their Probability Distribution

Question 1

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that x assumes a value from 2 to 5 is:

Answer 1

0.73

Question 2

A continuous random variable is a random variable:

A)that can assume any value in one or more intervals
B)whose set of values is countable
C)that is derived from a random population
D)that is determined by random probability

Answer 2

that can assume any value in one or more intervals

Question 3

For a discrete random variable x,the probability of any value of x is:

A)always greater than 1
B)always less than zero
C)always in the range zero to 1
D)never greater than zero

Answer 3

always in the range zero to 1

Question 4

A random variable is a variable whose value is determined by the:

A)outcome of a random experiment
B)random population
C)random space
D)random subjective probability

Question 5

For the probability distribution of a discrete random variable x,the sum of the probabilities of all values of x must be:

A)equal to zero
B)in the range zero to 1
C)equal to 0.5
D)equal to 1

Question 6

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that x is less than or equal to 5 is:

Question 7

Which of the following is an example of a discrete random variable?

A)The weight of a box of cookies
B)The length of a window frame
C)The number of horses owned by a farmer
D)The distance from home to work for a worker

Question 8

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that x is greater than or equal to 4 is:

Question 9

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability of is:

Question 10

The probability distribution table of a discrete random variable lists:

A)the bottom half of the values that the random variable can assume and their corresponding probabilities
B)all of the values that the random variable can assume and their corresponding probabilities
C)all of the values that the random variable can assume and their corresponding frequencies
D)the top half of the values that the random variable can assume and their corresponding frequencies

Question 11

Which of the following is true for the probability distribution of a discrete random variable x?

A)
B)
C)
D)

Question 12

Which of the following is not an example of a discrete random variable?

A)The number of days it rains in a month in New York
B)The number of stocks a person owns
C)The number of persons allergic to penicillin
D)The time spent by a physician with a patient

Question 13

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability of is:

Question 14

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that x is greater than 3 is:

Question 15

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that is less than or equal to 4 is:

Question 16

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that assumes a value from 3 to 6 is:

Question 17

Which of the following is true for the probability of a discrete random variable x?

A)
B)
C)
D)

Question 18

A discrete random variable is a random variable:

A)that can assume any value in one or more intervals
B)whose set of values is countable
C)that is derived from a random population
D)that is determined by random probability

Question 19

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that x is less than 5 is:

Question 20

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that is greater than or equal to 6 is:

Question 21

The formula used to obtain the mean of a discrete random variable is:

A)
B)
C)
D)

Question 22

The mean of a discrete random variable is its:

A)box-and-whisker measure
B)expected value
C)second quartile
D)upper hinge

Question 23

The mean of a discrete random variable is the mean of its:

A)frequency distribution
B)percentage distribution
C)probability distribution
D)second and third quartiles

Question 24

Use the following to answer questions :
The following table lists the probability distribution of the number of refrigerators owned by all families in a city.

The probability that a randomly selected family owns less than two refrigerators is:

Question 25

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The mean of the random variable x is:

Question 26

Use the following to answer questions 34-35:
The following table lists the probability distribution of a discrete random variable x:

The standard deviation of the random variable x,rounded to three decimal places,is:

Question 27

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that is greater than 6 is:

Question 28

A Bernoulli trial is:

A)the trial of a court case
B)a repetition of a binomial experiment
C)a repetition of a probability distribution
D)the trial of a probability distribution

Question 29

Use the following to answer questions :
The following table lists the probability distribution of the number of refrigerators owned by all families in a city.

The probability that a randomly selected family owns more than one refrigerator is:

Question 30

The standard deviation of a discrete random variable is the standard deviation of its:

A)frequency distribution
B)percentage distribution
C)probability distribution
D)first and fourth quartiles

Question 31

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The mean of the random variable x is:

Question 32

Use the following to answer questions 34-35:
The following table lists the probability distribution of a discrete random variable x:

The mean of the random variable x is:

Question 33

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The standard deviation of the random variable x,rounded to three decimal places,is:

Question 34

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The probability that is less than 4 is:

Question 35

Use the following to answer questions :
The following table lists the probability distribution of the number of HD-TVs owned by all families in a city.

The mean number of HD-TVs owned by these families is:

Question 36

Use the following to answer questions :
The following table lists the probability distribution of the number of refrigerators owned by all families in a city.

The probability that a randomly selected family owns exactly two refrigerators is:

Question 37

Use the following to answer questions :
The following table lists the probability distribution of the number of refrigerators owned by all families in a city.

The probability that a randomly selected family owns at most one refrigerator is:

Question 38

Use the following to answer questions :
The following table lists the probability distribution of the number of HD-TVs owned by all families in a city.

The standard deviation of the number of HD-TVs owned by these families,rounded to three decimal places,is:

Question 39

Use the following to answer questions :
The following table lists the probability distribution of the number of refrigerators owned by all families in a city.

The probability that a randomly selected family owns at least two refrigerators is:

Question 40

Use the following to answer questions :
The following table lists the probability distribution of a discrete random variable x:

The standard deviation of the random variable x,round to three decimal places,is:

Question 41

In binomial experiments,the outcome called a "success" is an outcome:

A)that is always beneficial
B)that is linked to success
C)to which the question refers
D)that is favorable

Question 42

Thirty-two percent of adults did not visit their physicians' offices last year.The probability,rounded to four decimal places,that in a random sample of 8 adults,exactly 3 will say they did not visit their physicians' offices last year is:

Question 43

The mean of a binomial distribution is equal to:

A)npq
B)np
C)square of npq
D)square root of npq

Question 44

The standard deviation of a binomial distribution is equal to:

A)npq
B)np
C)square of npq
D)square root of npq

Question 45

For 4.7,the probability of x = 3,rounded to four decimal places,is:

Question 46

The hypergeometric probability distribution can be used whenever:

A)a sample is drawn at random with replacement
B)successive trials are independent of each other
C)the probability of two outcomes remains constant
D)the population is finite and sampling occurs without replacement

Question 47

The binomial probability distribution is symmetric if:

A)p is equal to 0.25
B)p is equal to 0.50
C)p is less than 0.50
D)p is greater than 0.50

Question 48

The binomial probability distribution is right-skewed if:

A)p is 0.25 or smaller
B)p is equal to 0.50
C)p is less than 0.50
D)p is greater than 0.50

Question 49

Sixty percent of all children in a school do not have cavities.The probability,rounded to four decimal places,that in a random sample of 9 children selected from this school,at least 4 do not have cavities is:

Question 50

The parameter(s)of the Poisson probability distribution is(are):

A)
B)
C)
D)

Question 51

The binomial probability distribution is left-skewed if:

A)p is 0.25 or greater
B)p is equal to 0.50
C)p is less than 0.50
D)p is greater than 0.50

Question 52

The parameters of the binomial probability distribution are:

A)n,p,and q
B)n,p,q,and x
C)n,p,and x
D)n and p

Question 53

Which of the following is an example of a binomial experiment?

A)Rolling a die 10 times and observing for a number
B)Selecting five persons and observing whether they are in favor of an issue,against it,or have no opinion
C)Tossing a coin 20 times and observing for a head or tail
D)Drawing three marbles from a box that contains red,blue,and yellow marbles

Question 54

Which of the following is not a condition to apply the Poisson probability distribution?

A)x is a discrete random variable
B)There are n identical occurrences
C)The occurrences are random
D)The occurrences are independent

Question 55

Forty-four percent of customers who visit a department store make a purchase.The probability,rounded to four decimal places,that in a random sample of 12 customers who will visit this department store,exactly 7 will make a purchase is:

Question 56

Eight percent of all college graduates hired by companies stay with the same company for more than five years.The probability,rounded to four decimal places,that in a random sample of 11 such college graduates hired recently by companies,exactly 3 will stay with the same company for more than five years is:

Question 57

Which of the following is not a condition of the binomial experiment?

A)There are only two trials
B)Each trial has two and only two outcomes
C)p is the probability of success,q is the probability of failure,and
D)The trials are independent

Question 58

Which of the following is not a binomial experiment?

A)Rolling a die 25 times and observing for an even or odd number
B)Randomly selecting 50 items from a production line and observing if they are good or defective
C)Rolling a die 20 times and observing for a number that is less than or equal to 4 or greater than 4
D)Selecting 50 adults and observing if they are in favor of an issue,against it,or have no opinion

Question 59

Thirty percent of law students who sit for a bar exam pass it the first time.The probability,rounded to four decimal places,that in a random sample of 15 law students who will sit for the bar examination,at most 4 will pass it the first time is:

Question 60

Five percent of all credit card holders eventually become delinquent.The probability,rounded to four decimal places,that in a random sample of 21 credit card holders,exactly 3 will become delinquent is:

Question 61

For 3.5,the probability of P(x < 4),rounded to four decimal places,is:

Question 62

Let N = 15,r = 6,and n = 4.Using the hypergeometric probability distribution formula,find P(x = 0).Round your answer to four decimal places.

Question 63

For 4.7,the probability of P(x > 3),rounded to four decimal places,is:

Question 64

Use the following to answer questions :
Historical data indicates that Rickenbacker Airlines receives an average of 2.9 complaints per day.
What is the probability,rounded to four decimal places,that on a given day,Rickenbacker Airlines will receive less than 3 complaints?

Question 65

Let N = 10,r = 6,and n = 7.Using the hypergeometric probability distribution formula,find P(x = 0).Round your answer to four decimal places.

Question 66

All 10 of the orangutans at a certain zoo contract a very serious disease which claims 84% of its victims (if an orangutan contracts the disease,the probability that it will die is 0.84).What is the probability,rounded to four decimal places,that exactly 1 of the orangutans at this zoo will survive?

Question 67

The mean number of accidents to occur at a busy intersection during a 24-hour period has a Poisson distribution.If the probability of no accidents during a 24-hour period is 0.1165,what is the mean number of accidents,rounded to two decimal places,per 24-hour period?

Question 68

It costs $7.25 to play a very simple game,in which a dealer gives you one card from a deck of 52 cards.If the card is a heart,spade,or diamond,you lose.If the card is a club other than the queen of clubs,you win $11.50.If the card is the queen of clubs,you win $49.50.The random variable x represents your net gain from playing this game once,or your winnings minus the cost to play.What is the mean of x,rounded to the nearest penny?

Question 69

Use the following to answer questions :
A manufacturer packages bolts in boxes containing 100 each.Each box of 100 bolts contains,on average,6 defective bolts.The quality control staff randomly selects a box at the end of the day from an entire production run.
What is the probability,rounded to four decimal places,that the box will contain less than 7 defective bolts?

Question 70

The number of small air bubbles per 3 feet by 3 feet plastic sheet has a Poisson distribution with a mean number of 2.8 per sheet.What percent of these sheets have no air bubbles?

Question 71

Use the following to answer questions :
A manufacturer packages bolts in boxes containing 100 each.Each box of 100 bolts contains,on average,6 defective bolts.The quality control staff randomly selects a box at the end of the day from an entire production run.
What is the probability,rounded to four decimal places,that the box will contain at most 6 defective bolts?

Question 72

A survey of 1,000 households gives the probability distribution: Is this a valid probability distribution?

A)Yes
B)No

Question 73

A survey show that out of 1,000 households surveyed,392 own one car,432 own two cars,153 own three cars,and 23 own 4 or more cars.Construct the probability distribution for this data.

Question 74

Use the following to answer questions :
Historical data indicates that Rickenbacker Airlines receives an average of 2.9 complaints per day.
What is the probability,rounded to four decimal places,that on a given day,Rickenbacker Airlines will receive at least 5 complaints?

Question 75

Let N = 15,r = 5,and n = 2.Using the hypergeometric probability distribution formula,find P(x 1).Round your answer to four decimal places.

Question 76

Use the following to answer questions :
A manufacturer packages bolts in boxes containing 100 each.Each box of 100 bolts contains,on average,6 defective bolts.The quality control staff randomly selects a box at the end of the day from an entire production run.
What is the probability,rounded to four decimal places,that the box will contain exactly 7 defective bolts?

Question 77

Use the following to answer questions :
Historical data indicates that Rickenbacker Airlines receives an average of 2.9 complaints per day.
What is the probability,rounded to four decimal places,that on a given day,Rickenbacker Airlines will receive exactly 1 complaints?