Deck 5: Discrete Random Variables

Question 1

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

Answer 1

False

Question 2

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.

Answer 2

False

Question 3

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

Answer 3

False

Question 4

The binomial distribution is characterized by situations that are analogous to

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

Question 5

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

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

Question 6

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

A)
B)
C)
D)

Question 7

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 8

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 9

A random variable is said to be discrete if

A)Its outcomes are countable
B)It can assume any real number within a given interval
C)The rules of probability apply
D)It can be represented graphically

Question 10

In a binomial distribution the random variable X is continuous.

Question 11

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

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

Question 12

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 13

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 defectives is given most likely by ___________________ distribution.

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

Question 14

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

Question 15

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 16

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

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

Question 17

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 18

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 19

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes,what is the probability that exactly 4 cars will arrive in a five minute interval?

A)Binomial
B)Poisson
C)Both of the above
D)None of the above

Question 20

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 is an example of a discrete random variable.

Question 21

If n = 20 and p = .4,then the mean of the binomial distribution is

A).4
B)4.8
C)8
D)12

Question 22

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 23

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 24

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 25

The Securities and Exchange Commission has determined that the number of companies listed in 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 26

The manager of the local grocery store has determined that,on the 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 27

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

A)Always
B)Sometimes
C)Never

Question 28

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

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

Question 29

The Securities and Exchange Commission has determined that the number of companies listed in 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 30

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

A)9
B)6
C)3.6
D)1.8974
E).4

Question 31

In the most recent election,19% 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 32

In the most recent election,19% 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 33

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 34

Two characteristics/assumptions of the Poisson distribution include:

A)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 non-overlapping 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 non-overlapping interval,and the random variable of interest is discrete.
D)The event occurring in one interval is dependent of the event occurring in any other non-overlapping interval,and the random variable of interest is continuous.

Question 35

Of all individual tax returns,37% 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)
B)
C)
D)

Question 36

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

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

Question 37

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 38

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 39

The manager of the local grocery store has determined that,on the 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 40

According to a survey of adults,64% have money in a regular savings account.If we plan on surveying 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 41

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10%. 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 42

The variable "employment status" which can take on one of two values: 1 for "employed" and 0 for "unemployed" is an example of a _____________ random variable.

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

Question 43

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 44

In a study conducted by UCLA,it was found that 25% of college freshmen support increased military spending.If 6 college freshmen are randomly selected,find the probability that: Only 1 support increased military spending

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

Question 45

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10%. 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 46

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

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

Question 47

In a study conducted by UCLA,it was found that 25% of college freshmen support increased military spending.If 6 college freshmen are randomly selected,find the probability that: Exactly 3 support increased military spending

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

Question 48

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 nearest whole number).

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

Question 49

In a study conducted for the State Department of Education,30% 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 50

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10%. 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 51

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

A)np
B)(npq)²
C) $\sqrt{npq}$
D)npq

Question 52

It is known that 15% of all college freshmen at Ivey University leave after their first year.Calculate the interval that contains 99.73% of the students who remain if we are looking at a random sample of 300 Ivey University freshmen.

A)[236.45 273.55]
B)[26.45 63.55]
C)[110.25 369.75]
D)[38.82 51.18]

Question 53

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

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

Question 54

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 55

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 56

Historical data shows 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 Poisson distribution. Determine the probability of 6 patients arriving in a five-hour period.

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

Question 57

In a study conducted by UCLA,it was found that 25% of college freshmen support increased military spending.If 6 college freshmen are randomly selected,find the probability that: Fewer than 4 support increased military spending

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

Question 58

A company manufactures an appliance,gives a warranty and 95% of its appliances do not require repair before the warranty expires.If an organization buys 10 of these appliances,calculate an interval that contains 95.44% of all the appliances that won't require repair.

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

Question 59

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 60

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 61

Historical data shows 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 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 62

A vaccine is 95 percent effective.What is the probability that it is not effective for: More than one out of 20 individuals?

A).7359
B).3585
C).2641
D).3774

Question 63

Assume the number of trucks passing an intersection has a Poisson distribution with mean of 5 trucks per minute.What is the probability of 0 or 1 trucks in one minute?

A).0404
B).0337
C).0842
D).0067

Question 64

For a binomial process,the probability of success is 40% and the number of trials is 5. Find the standard deviation.

A)5.0
B)1.2
C)2.0
D)1.1

Question 65

The number of calls coming into a PBX follows a Poisson process with a mean of 120 calls per hour.What is the probability of no calls in a one-minute interval?

A)0
B).1353
C).4060
D).3679

Question 66

During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute.The arrivals are distributed according to the Poisson distribution. What is the probability that during the next five minutes three cars will arrive?

A).2138
B).1804
C).0126
D).0613

Question 67

If x is a Poisson random variable with a mean of 10,what is the probability that x is greater than or equal to 2?

A).9972
B).0028
C).9995
D).0005

Question 68

If x is a Poisson random variable with a mean of 10,what is the probability that x is greater than 6?

A).9329
B).7797
C).8698
D).0002

Question 69

For a binomial process,the probability of success is 40% and the number of trials is 5. Find the variance.

A)5.0
B)1.2
C)2.0
D)1.1

Question 70

If the probability distribution of X is: What is the expected value of X?

A)1.0
B)5.0
C)2.25
D)2.24

Question 71

During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute.The arrivals are distributed according to the Poisson distribution. What is the probability that during the next minute three cars will arrive?

A).0758
B).1255
C).0126
D).0613

Question 72

A vaccine is 95 percent effective.What is the probability that it is not effective for: One and only one individual out of 20 individuals?

A).0179
B).3585
C).0189
D).3774

Question 73

For a binomial process,the probability of success is 40% and the number of trials is 5. Find the expected value.

A)5.0
B)1.2
C)2.0
D)1.1

Question 74

If the probability of a success on a single trial is .2,what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

A).0031
B).5033
C).1074
D).2013

Question 75

Determine the probability that a 3 will appear twice,if a fair die is rolled 10 times.

A).5010
B).2907
C).2318
D).0065

Question 76

A test has 6 multiple choice questions,each with 4 alternatives.What is the probability of guessing 5 or more questions correctly?

A).5340
B).4660
C).9954
D).0046

Question 77

Twenty coins are tossed.What is the probability of getting exactly 10 heads?

A).3364
B).1602
C).5000
D).1762

Question 78

If the probability distribution of X is: What is the variance of X?

A)1.0
B)5.0
C)2.25
D)2.24

Question 79

Three candidates run for different offices in different counties.Each has a one in three chance of being elected in his/her county.What is the probability that at least one of them will be elected?

A).2963
B).7037
C).33
D).667

Question 80

If x is a Poisson random variable with a mean of 10,what is the probability that x is equal to 8?

A).1126
B).1251
C).2677
D).0993