Deck 5: Discrete Random Variables

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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.

Question 7

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 8

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

Question 9

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 10

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

Question 11

The variable Home Ownership can take on one of two values,1 if the person living in a home owns the home and 0 if the person living in a home does not own the home.This is an example of a discrete random variable.

Question 12

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

Question 13

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 14

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 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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 22

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 23

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

A) right skewed
B) left skewed
C) symmetric
D) bimodal

Question 24

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 _________________ distribution(s).

A) the binomial
B) the Poisson
C) the hypergeometric
D) both the binomial and Poisson

Question 25

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 26

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

A)
B)

C)

D)

Question 27

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 items that are sampled without replacement.
D) the number of items in the sample that are successes.

Question 28

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 29

A random variable

A) is the result of a measurement.
B) can only be discrete.
C) assigns one and only one numeric value to each experimental outcome.
D) is a binomial,Poisson,or hypergeometric variable.

Question 30

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 31

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 32

The mean of a hypergeometric random variable is defined as

A) n × (r/N).
B) N × (r/n).
C) npq.
D) np.

Question 33

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

A) right skewed
B) left skewed
C) symmetric
D) bimodal

Question 34

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 35

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 36

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 37

A discrete probability distribution is expressed as a table,graph,or ___________ that gives the probability associated with each possible value that the random variable can assume.

A) binomial
B) formula
C) Poisson
D) hypergeometric

Question 38

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 four cars will arrive in a 5-minute interval?

A) binomial
B) Poisson
C) both binomial and Poisson
D) neither binomial nor Poisson

Question 39

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 40

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 41

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

A) binomial
B) Poisson
C) hypergeometric
D) continuous

Question 42

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 43

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 44

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

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 45

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 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

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

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

Question 48

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 49

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

A) always
B) sometimes
C) never

Question 50

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 51

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 52

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 53

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 54

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 55

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 56

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 57

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 58

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 59

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 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

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 62

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 63

The J.O.Supplies Company buys calculators from a non-US 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

The J.O.Supplies Company buys calculators from a non-US 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 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

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 67

The J.O.Supplies Company buys calculators from a non-US 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 68

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 69

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 70

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 71

A multiple-choice test has 30 questions and each one has five possible answers,of which only 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