Deck 5: Discrete Random Variables

Question 1

For a discrete probability distribution,the value of p(x)for each value of x falls between -1 and 1.

Answer 1

False

Question 2

The mean and the variance of a Poisson random variable are equal.

Answer 2

True

Question 3

If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.

Answer 3

False

Question 4

A correlation coefficient is a unitless measure of the linear relationship between two random variables.

Question 5

The expected value of the discrete random variable x is the population mean.

Question 6

In a hypergeometric probability distribution of a population of N items,r refers to the number of successes and N - r to the number of failures.

Question 7

With two random variables x and y,a positive covariance says that as x increases,y tends to increase in a linear fashion.

Question 8

A discrete random variable may assume a countable number of outcome values.

Question 9

If the population size is at least 20 times larger than the sample size,a hypergeometric distribution can be approximated by the binomial distribution.

Question 10

In a binomial distribution,the random variable X is continuous.

Question 11

The binomial experiment consists of n independent,identical trials,each of which results in either success or failure and is such that the probability of success on any trial is the same.

Question 12

Depending on the mean of the Poisson distribution,the distribution can either be very skewed to the right or quite symmetrical.

Question 13

The mean of the binomial distribution is np(1 - p).

Question 14

In a binomial experiment,the results of one trial are dependent on the results of other trials.

Question 15

The internal auditor for your company believes that 10 percent of their invoices contain errors.To check this theory,20 invoices are randomly selected and 5 are found to have errors.The claim of the auditor will be rejected.

Question 16

The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

Question 17

The hypergeometric probability distribution can be approximated by the Poisson distribution.

Question 18

A Poisson random variable is a continuous variable that can be used to describe the number of occurrences of an event over a specified interval of time or space.

Question 19

The variable Home Ownership can take on one of two values,1 if the person living in a home owns the home and zero if the person living in a home does not own the home.This is an example of a discrete random variable.

Question 20

The time (in seconds)it takes for an athlete to run 50 meters is an example of a continuous random variable.

Question 21

A hypergeometric random variable x has a distribution that is approximated by a binomial distribution when:

A)The number of successes is larger than the number of failures in the population.
B)A sample is selected from the population without replacement.
C)The population is much larger than the sample size.
D)The sample size is half the size of the original population.

Question 22

The random variable x has a hypergeometric distribution,and the population contains 12 items.If you wanted to find the number of defects in a random sample of 3 selected items when the population contains 5 defects,identify the N,n,and r.

A)N = 3,n = 12,r = 5
B)N = 5,n = 12,r = 7
C)N = 12,n = 5,r = 3
D)N = 12,n = 3,r = 5

Question 23

Which one of the following statements is not an assumption of the binomial distribution?

A)Sampling is with replacement.
B)The experiment consists of n identical trials.
C)The probability of success remains constant from trial to trial.
D)Trials are independent of each other.
E)Each trial results in one of two mutually exclusive outcomes.

Question 24

A random variable:

A)Is the result of a measurement.
B)Can only be discrete.
C)Can be thought of as representing an uncertain numerical outcome to an experiment.
D)Is a binomial,Poisson,or hypergeometric variable.

Question 25

A probability distribution of a discrete random variable is expressed as a table,graph,or ___________.

A)Binomial
B)Formula
C)Poisson
D)Hypergeometric

Question 26

The mean of a hypergeometric random variable is defined as:

A)n × (r/N)
B)N × (r/n)
C)npq
D)np

Question 27

The mean of the binomial distribution is equal to:

A)p
B)np
C)p^x(1 - p)^n-x
D)(n)(p)(1 - p)
E)

Question 28

Using the following probability distribution table of the random variable x,what is the probability of x = 3?

A)3/15
B)5/15
C)1/15
D)2/15

Question 29

Which of the following is not a discrete random variable?

A)The number of times a light changes red in a 10-minute cycle.
B)The number of minutes required to run 1 mile.
C)The number of defects in a sample selected from a population of 100 products.
D)The number of criminals found in a five-mile radius of a neighborhood.

Question 30

The number of ways to arrange x successes among n trials is equal to:

A)Option A
B)Option B
C)Option C
D)Option D

Question 31

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-through fast-food restaurant is three in 10 minutes.What is the probability that exactly 4 cars will arrive in a five-minute interval?

A)Binomial
B)Poisson
C)Both of these
D)None of these

Question 32

In the context of the hypergeometric distribution,r is

A)Sample size.
B)The number of items in the population that are successes.
C)The number of times items that are sampled without replacement.
D)The number of items in the sample that are successes.

Question 33

If the number of surface nonconformities on a specific size of metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 defects is given most likely by the _________________ distribution.

A)Binomial
B)Poisson
C)Hypergeometric
D)Both binomial and poisson

Question 34

The probability distribution of a random variable that is defined to be the number of successes obtained in a random sample selected without replacement from a finite population of N elements that contains r successes and N - r failures is:

A)Poisson
B)Binomial
C)Hypergeometric
D)Discrete

Question 35

The property of expected values says if a and b are constants,and if x and y are random variables,then μ_{(ax + by)} = aμ_x + bμ_y + 2ab.

Question 36

The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.

A)Binomial
B)Uniform
C)Normal
D)Poisson

Question 37

Which of the following is a valid probability value for a discrete random variable?

A).2
B)1.01
C)-.7
D)All of these

Question 38

A total of 50 raffle tickets are sold for a contest to win a car.If you purchase one ticket,what are your odds against winning?

A)49 to 1
B)50 to 1
C).05
D).01

Question 39

If p = .1 and n = 5,then the corresponding binomial distribution is ____________.

A)Right skewed
B)Left skewed
C)Symmetric
D)Bimodal

Question 40

If p = .5 and n = 4,then the corresponding binomial distribution is ____________.

A)Right skewed
B)Left skewed
C)Symmetric
D)Bimodal

Question 41

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month.Find the probability that more than 1 bankruptcy occurs next month.

A).1931
B).9257
C).7326
D).4816
E).2674

Question 42

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month.Find the probability that exactly 4 bankruptcies occur next month.

A).8774
B).1414
C).1557
D).2176

Question 43

If n = 15 and p = .4,then the standard deviation of the binomial distribution is:

A)9
B)6
C)3.6
D)1.897
E).4

Question 44

The requirement that the probability of success remains constant from trial to trial is a property of the _______________ distribution.

A)Binomial
B)Poisson
C)Hypergeometric
D)Continuous

Question 45

If x is a binomial random variable,then the standard deviation of x is given by:

A)np
B)(npq)²
C)√npq
D)npq

Question 46

A fair die is rolled 10 times.What is the average number of even number outcomes?

A)3
B)4
C)5
D)6
E)7

Question 47

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6)outcomes?

A)18
B)9
C)5
D)3
E)1.732

Question 48

The binomial distribution is characterized by situations that are analogous to

A)Drawing balls from an urn.
B)Coin tossing.
C)Counting defects on an item.
D)Measuring the length of an item.

Question 49

The equation for the variance of the binomial distribution is given by:

A)p^x(1 - p)^n-x
B)np
C)np(1 - p)
D)

Question 50

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month.Find the probability that no more than one bankruptcy occurs next month.

A).1931
B).9257
C).7326
D).4816
E).2674

Question 51

A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5)will occur fewer than 3 times?

A).0547
B).1172
C).1550
D).7752
E).8450

Question 52

When p = .5,the binomial distribution will _________ be symmetric.

A)Always
B)Sometimes
C)Never

Question 53

Two characteristics,or assumptions,of the Poisson distribution are:

A)The probability of success remains constant from trial to trial,and the random variable of interest is continuous.
B)The event occurring in one interval is independent of the event occurring in any other nonoverlapping interval,and the random variable of interest is continuous.
C)The event occurring in one interval is independent of the event occurring in any other nonoverlapping interval,and the random variable of interest is discrete.
D)The event occurring in one interval is dependent on the event occurring in any other nonoverlapping interval,and the random variable of interest is continuous.

Question 54

Which of the following statements about the binomial distribution is not correct?

A)Each trial results in a success or failure.
B)Trials are independent of each other.
C)The probability of success remains constant from trial to trial.
D)The random variable of interest is continuous.
E)The experiment consists of n identical trials.

Question 55

A fair die is rolled 10 times.What is the probability that an even number (2,4,or 6)will occur between 2 and 4 times?

A).6123
B).1709
C).1611
D).3662
E).3223

Question 56

For a random variable X,the mean value of the squared deviations of its values from their expected value is called its ____________.

A)Standard deviation
B)Mean
C)Probability
D)Variance

Question 57

A random variable that is defined to be the total number of successes in n trials is a __________ random variable.

A)Binomial
B)Poisson
C)Hypergeometric
D)Continuous

Question 58

The variable Employment Status,which can take either the value 1 for Employed and 0 for Unemployed,is an example of a _____________ random variable.

A)Poisson
B)Discrete
C)Hypergeometric
D)Continuous

Question 59

The distribution whose mean is equal to its variance is the _________ distribution.

A)Binomial
B)Poisson
C)Hypergeometric
D)Continuous

Question 60

A discrete variable that can often be used to describe the number of occurrences of an event over a specified interval of time or space is a ___________ random variable.

A)Poisson
B)Discrete
C)Hypergeometric
D)Continuous

Question 61

The probability that a given computer chip will fail is 0.02.Find the probability that of 5 delivered chips,exactly 2 will fail.

A).9039
B).0922
C).0038
D).0000

Question 62

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number).

A)56
B)35
C)29
D)25

Question 63

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

A).0702
B).2639
C).0016
D)0

Question 64

An appliance manufacturer gives a warranty,and 95 percent of its appliances do not require repair before the warranty expires.An organization buys 10 of these appliances.Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

A)[8.12,10.88]
B)[7.43,11.57]
C)[8.81,10.19]
D)[8.55,10.45]

Question 65

Of all individual tax returns,37 percent include errors made by the taxpayer.If IRS examiners are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

A)μ = 2.80,σ = 1.67
B)μ = 4.44,σ = 1.67
C)μ = 4.44,σ = 2.80
D)μ = 7.56,σ = 2.80

Question 66

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

A)9.00
B)3.17
C)9.49
D)3.00

Question 67

In the most recent election,19 percent of all eligible college students voted.If a random sample of 20 students were surveyed,find the probability that none of the students voted.

A).0000
B).0014
C).0148
D).4997

Question 68

In a study conducted for the state Department of Education,30 percent of the teachers who left teaching did so because they were laid off.Assume that we randomly select 10 teachers who have recently left their profession.Find the probability that exactly 4 of them were laid off.

A).3000
B).2668
C).2001
D).0090

Question 69

The manager of the local grocery store has determined that,on average,4 customers use the service desk every half-hour.Assume that the number of customers using the service desk has a Poisson distribution.What is the probability that during a randomly selected half-hour period,no more than 2 customers use the service desk?

A).2381
B).1465
C).7619
D).8535
E).0916

Question 70

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the expected number of defectives?

A)9
B)90
C)10
D)95

Question 71

In the most recent election,19 percent of all eligible college students voted.If a random sample of 20 students were surveyed,find the probability that exactly half voted in the election.

A).0000
B).0014
C).0148
D).4997

Question 72

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that fewer than 4 support increased spending on environmental issues.

A).0330
B).7844
C).9624
D).9954

Question 73

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours.Assume that the patient arrivals are distributed according to a Poisson distribution.Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period.

A).3813
B).5711
C).4276
D).7861
E).6174

Question 74

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

A).0604
B).1325
C).2552
D).8000

Question 75

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that exactly 3 support increased spending on environmental issues.

A).0330
B).1318
C).7844
D).9624

Question 76

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that only 1 supports increased spending on environmental issues.

A).0330
B).1318
C).3560
D).7844

Question 77

According to a survey of adults,64 percent have money in a regular savings account.If we were to survey 50 randomly selected adults,find the mean number of adults who would have regular savings accounts.

A)12
B)22
C)32
D)42

Question 78

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 3 calculators are selected at random,what is the probability that one of the calculators will be defective?

A).0702
B).0010
C).2430
D).7290

Question 79

The manager of the local grocery store has determined that,on average,4 customers use the service desk every half-hour.Assume that the number of customers using the service desk has a Poisson distribution.What is the probability that during a randomly selected half-hour period,exactly 2 customers use the service desk?

A).0183
B).0733
C).1465
D).9084
E).7619

Question 80

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two hours.Assume that the patient arrivals are distributed according to a Poisson distribution.Determine the probability of 6 patients arriving in a five-hour period.

A).136
B).109
C).246
D).001