Deck 4: Discrete Random Variables

Question 1

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

A) $n / x!$
B) $\frac { n ! } { ( n - x ) ! }$
C) $n / x$
D) $n ! / x !$
E) $\frac { n ! } { x ! ( n - x ) ! }$

Answer 1

$\frac { n ! } { x ! ( n - x ) ! }$

Question 2

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

Answer 2

True

Question 3

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 3

False

Question 4

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)Hypergeometric
D)Normal
E)Uniform

Question 5

The mean of the binomial distribution is equal to:

A)p
B)np
C)px(1 - p)n-x
D)npq
E) $\sqrt { n p q }$

Question 6

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)normal
E)exponential

Question 7

In a binomial distribution the random variable X is continuous.

Question 8

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
E)hypergeometric

Question 9

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 10

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

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

Question 11

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the expected number of black balls?

A)25.42
B)23.76
C)21.43
D)19.94
E)17.30

Question 12

The mean of the binomial distribution with n trials and probability of success p is np(1 - p).

Question 13

When using hypergeometric distribution,it is assumed that the trials are __________ and the probability of success ________ from trial to trial.

A)independent,does not change
B)dependent,does not change
C)independent,changes
D)dependent,changes

Question 14

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 15

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

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

Question 16

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

Question 17

The hypergeometric distribution is appropriate when sampling with replacement from small populations

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

A store owner records the number of customers who make a purchase for the first five customers during a particular day.In this situation,X may be 0,1,2,3,4,or 5.

Question 20

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the probability that exactly 20 of them will be black balls?

A)0.2581
B)0.3861
C)0.6667
D)0.1573
E)0.4770

Question 21

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 22

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 23

Find the probability that no more than one bankruptcy occurs next year.

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

Question 24

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.
E)Probability of success remains changes from trial to trial and the random variable of interest is continuous.

Question 25

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

A)9039
B)0922
C)0012
D)0000
E)0038

Question 26

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

A)4
B)4.8
C)8
D)12
E)24

Question 27

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 28

Find the probability that exactly 4 bankruptcies occur next year.

A)8774
B)1414
C)1557
D)2176
E)2500

Question 29

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.
E)It represents a qualitative variable.

Question 30

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the standard deviation of the number of black balls?

A)3.55
B)1.88
C)4.24
D)2.85
E)4.62

Question 31

Find the probability that more than 1 bankruptcy occurs next year.

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

Question 32

According to a survey of adults,64% have money in a regular savings account independent of other adults.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
E)46

Question 33

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 34

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

A)always
B)sometimes
C)never

Question 35

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)0.6123
B)0.1709
C)0.1611
D)0.3662
E)0.3223

Question 36

A fair die is rolled 10 times.What is the average number of even number (2,4,or 6)outcomes?

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

Question 37

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

A)We sample without replacement from a small population.
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 38

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 39

Which of the following variables could be a binomial random variable?

A)The number potholes in a 10 km stretch of road.
B)The number of heads you obtain when you flip a coin 10 times.
C)The height of a randomly chosen student.
D)The number of defects in a car's paint.
E)Tomorrow's high temperature.

Question 40

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

A)p
B)np
C)px(1 - p)n-x
D)npq
E) $\sqrt { n p q }$

Question 41

Find the probability that none of the students voted.

A)0.0000
B)0.0014
C)0.0148
D)0.2500
E)0.4997

Question 42

According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?

A)0002
B)0243
C)0378
D)0467
E)0697

Question 43

Find the probability that exactly half voted in the election.

A)0.0000
B)0.0014
C)0.0148
D)0.2500
E)0.4997

Question 44

If 100 calculators are selected at random,what is the expected number of defectives?

A)2
B)4
C)6
D)8
E)10

Question 45

If 3 calculators are selected at random,what is the probability that one of the calculators will be defective?

A)003
B)055
C)167
D)243
E)333

Question 46

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

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

Question 47

What is the probability that exactly 4 of the jobs were not completed within the bid time?

A)0472
B)1361
C)2293
D)3471
E)4441

Question 48

A class of 20 students;8 male and 12 female.If you select 8 students at random,what is the probability that at least 3 of them will be male?

A)0.4000
B)0.7404
C)0.7496
D)0.2504
E)0.2596

Question 49

Determine the probability of 6 patients arriving in a five-hour period.

A)019
B)136
C)233
D)369
E)401

Question 50

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
E)16

Question 51

If the probability distribution of X is:
$$\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$$

-What is the variance of X?

A)1
B)2
C)3
D)4
E)5

Question 52

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 53

If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

A)1.5
B)2.0
C)2.5
D)3.0
E)3.5

Question 54

Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period.

A)281
B)708
C)898
D)617
E)463

Question 55

If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

A)0702
B)1134
C)2365
D)3395
E)4662

Question 56

If the probability distribution of X is:
$$\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$$

-What is the expected value of X?

A)1
B)2
C)3
D)4
E)5

Question 57

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

A) $\mu$ = 2.80, $\sigma$ = 1.67
B) $\mu$ = 3.70, $\sigma$ = 1.67
C) $\mu$ = 4.44, $\sigma$ = 1.67
D) $\mu$ = 4.44, $\sigma$ = 2.80
E) $\mu$ = 7.56, $\sigma$ = 2.80

Question 58

What is the mean number of jobs completed within the bid time?

A)1.3
B)8.3
C)2.4
D)4.3
E)3.4

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)2000
D)2552
E)8000

Question 60

In a study conducted for a local union,30% of the employees who became unemployed in the last year did so because they were laid off.Assume that we randomly select 10 employees who have recently left their position.Find the probability that exactly 4 of them were laid off.

A)3000
B)2668
C)2001
D)0090
E)0009

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 6 patients arriving in a five-hour period.

Question 62

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

Question 63

If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

Question 64

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

Question 65

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?

Question 66

If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

Question 67

If 3 calculators are selected at random,what is the probability that exactly one of the calculators will be defective?

Question 68

More than one out of 20 individuals?

Question 69

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.

Question 70

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

Question 71

The hypergeometric distribution is used when sampling _____ replacement from small populations

Question 72

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

Question 73

If 100 calculators are selected at random,what is the expected number of defectives?

Question 74

If you roll a die 20 times,the number of times you roll a six is an example of a ________ random variable.

Question 75

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?

Question 76

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

Question 77

One and only one individual out of 20 individuals?

Question 78

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?

Question 79

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

Question 80

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(n)_____ random variable.