Deck 7: Random Variables and Discrete Probability Distributions

Question 1

The Poisson probability distribution is a continuous probability distribution.

Answer 1

False

Question 2

In a(n) ____________________ experiment, the probability of a success in an interval is the same for all equal-sized intervals.

Answer 2

Poisson

Question 3

In a Poisson distribution, the mean and standard deviation are equal.

Answer 3

False

Question 4

The Sutton police department must write, on average, 6 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.

A)The mean has no interpretation.
B)The expected number of tickets written would be 6.5 per day.
C)Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
D)The number of tickets that is written most often is 6.5 tickets per day.

Question 5

The number of accidents that occur at a busy intersection in one month is an example of a Poisson random variable.

Question 6

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Question 7

The largest value that a Poisson random variable X can have is n.

Question 8

The mean of a Poisson distribution, where $\mu$ is the average number of successes occurring in a specified interval, is $\mu$ .

Question 9

On the average, 1.6 customers per minute arrive at any one of the checkout counters of Sunshine food market. What type of probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in 10 minutes?

A)Poisson distribution
B)Normal distribution
C)Binomial distribution
D)None of these choices.

Question 10

The Poisson random variable is a:

A)discrete random variable with infinitely many possible values.
B)discrete random variable with finite number of possible values.
C)continuous random variable with infinitely many possible values.
D)continuous random variable with finite number of possible values.

Question 11

The Poisson random variable is a discrete random variable with infinitely many possible values.

Question 12

In a Poisson distribution, the variance and standard deviation are equal.

Question 13

In a Poisson experiment, the number of successes that occur in any interval of time is ____________________ of the number of success that occur in any other interval.

Question 14

In a Poisson distribution, the:

A)mean equals the standard deviation.
B)median equals the standard deviation.
C)mean equals the variance.
D)None of these choices.

Question 15

Which of the following cannot have a Poisson distribution?

A)The length of a movie.
B)The number of telephone calls received by a switchboard in a specified time period.
C)The number of customers arriving at a gas station in Christmas day.
D)The number of bacteria found in a cubic yard of soil.

Question 16

Given a Poisson random variable X, where the average number of successes occurring in a specified interval is 1.8, then P(X = 0) is:

A)1.8
B)1.3416
C)0.1653
D)6.05

Question 17

In a Poisson distribution, the mean and variance are equal.

Question 18

A community college has 150 word processors. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 25 of the word processors will require repair, one will use what type of probability distribution?

A)Normal distribution
B)Poisson distribution
C)Binomial distribution
D)None of these choices.

Question 19

The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

Question 20

The number of customers making a purchase out of 30 randomly selected customers has a Poisson distribution.

Question 21

In a Poisson experiment, the probability of a success in an interval is ____________________ to the size of the interval.

Question 22

NARRBEGIN: 911 Phone Calls
911 Phone Calls
911 phone calls arrive at the rate of 30 per hour at the local call center.NARREND

-{911 Phone Calls Narrative} If no calls are currently being processed, what is the probability that the desk employee can take four minutes break without being interrupted?

Question 23

Compute the following Poisson probabilities (to 4 decimal places) using the Poisson formula:
a.P(X = 3), if $\mu$ = 2.5
b.P(X $\le$ 1), if $\mu$ = 2.0
c.P(X $\ge$ 2), if $\mu$ = 3.0

Question 24

In the Poisson distribution, the mean is equal to the ____________________.

Question 25

A Poisson random variable is a(n) ____________________ random variable.

Question 26

NARRBEGIN: Post office
Post office
The number of arrivals at a local post office between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12.NARREND

-{{Post Office Narrative} Find the probability that the number of arrivals between 4:00 and 5:00 P.M. is exactly two.

Question 27

Let X be a Poisson random variable with $\mu$ = 6. Use the table of Poisson probabilities to calculate:
a.P(X $\le$ 8)
b.P(X = 8)
c.P(X $\ge$ 5)
d.P(6 $\le$ X $\le$ 10)

Question 28

NARRBEGIN: Post office
Post office
The number of arrivals at a local post office between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12.NARREND

-{Post Office Narrative} Find the probability that the number of arrivals between 3:00 and 5:00 P.M. is at least 10.

Question 29

The possible values of a Poisson random variable start at ____________________.

Question 30

A Poisson random variable is the number of successes that occur in a period of ____________________ or an interval of ____________________ in a Poisson experiment.

Question 31

NARRBEGIN: 911 Phone Calls
911 Phone Calls
911 phone calls arrive at the rate of 30 per hour at the local call center.NARREND

-{911 Phone Calls Narrative} Find the probability of receiving two calls in a five-minute interval of time.

Question 32

NARRBEGIN: Classified Department Pho
Classified Department Phone Calls
A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another.NARREND

-{Classified Department Phone Calls Narrative} Find the probability that the department will receive at least five calls between 2 and 4 P.M. on a particular afternoon.

Question 33

The ____________________ of a Poisson distribution is the rate at which successes occur for a given period of time or interval of space.

Question 34

NARRBEGIN: Post office
Post office
The number of arrivals at a local post office between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12.NARREND

-{Post Office Narrative} Find the probability that the number of arrivals between 3:30 and 4:00 P.M. is at least 10.

Question 35

In Poisson experiment, the probability of more than one success in an interval approaches ____________________ as the interval becomes smaller.

Question 36

NARRBEGIN: Classified Department Pho
Classified Department Phone Calls
A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another.NARREND

-{Classified Department Phone Calls Narrative} Find the probability that the department will receive 13 calls between 2 and 4 P.M. on a particular afternoon.

Question 37

Let X be a Poisson random variable with $\mu$ = 8. Use the table of Poisson probabilities to calculate:
a.P(X $\le$ 6)
b.P(X = 4)
c.P(X $\ge$ 3)
d.P(9 $\le$ X $\le$ 14)

Question 38

NARRBEGIN: Classified Department Pho
Classified Department Phone Calls
A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another.NARREND

-{Classified Department Phone Calls Narrative} Find the probability that the department will receive seven calls between 2 and 3 P.M. on a particular afternoon.

Question 39

In the Poisson distribution, the ____________________ is equal to the variance.

Question 40

NARRBEGIN: 911 Phone Calls
911 Phone Calls
911 phone calls arrive at the rate of 30 per hour at the local call center.NARREND

-{911 Phone Calls Narrative} Find the probability of receiving exactly eight calls in 15 minutes.

Question 41

The expected number of heads in 100 tosses of an unbiased coin is

A)25
B)50
C)75
D)100

Question 42

The binomial distribution deals with consecutive trials, each of which has two possible outcomes.

Question 43

NARRBEGIN: Post office
Post office
The number of arrivals at a local post office between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12.NARREND
Suppose that the number of buses arriving at a Depot per minute is a Poisson process. If the average number of buses arriving per minute is 3, what is the probability that exactly 6 buses arrive in the next minute?

Question 44

The standard deviation of a binomial random variable X is given by the formula $\sigma$ ²= np(1 - p), where n is the number of trials, and p is the probability of success.

Question 45

NARRBEGIN: Unsafe Levels of Radioact
Unsafe Levels of Radioactivity
The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND
{Unsafe Levels of Radioactivity Narrative} Find the standard deviation of the number of incidents is in one year.

Question 46

NARRBEGIN: Unsafe Levels of Radioact
Unsafe Levels of Radioactivity
The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND
{Unsafe Levels of Radioactivity Narrative} Find the probability that there will be exactly 3 incidents in a year.

Question 47

If the probability of success p remains constant in a binomial distribution, an increase in n will increase the variance.

Question 48

NARRBEGIN: Unsafe Levels of Radioact
Unsafe Levels of Radioactivity
The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND
{Unsafe Levels of Radioactivity Narrative} Find the variance of the number of incidents in one year.

Question 49

If X is a binomial random variable with n = 25, and p = 0.25, then P(X = 25) = 1.0.

Question 50

NARRBEGIN: Unsafe Levels of Radioact
Unsafe Levels of Radioactivity
The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND
{Unsafe Levels of Radioactiviy Narrative} Find the probability that there will be at least 1 incident in a year.

Question 51

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Question 52

The number of female customers out of a random sample of 100 customers arriving at a department store has a binomial distribution.

Question 53

The expected number of heads in 250 tosses of an unbiased coin is 125.

Question 54

The binomial random variable is the number of successes that occur in a fixed period of time.

Question 55

NARRBEGIN: Unsafe Levels of Radioact
Unsafe Levels of Radioactivity
The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND
{Unsafe Levels of Radioactivity Narrative} Find the probability that there will be at least 3 incidents in a year.

Question 56

The number of customers arriving at a department store in a 5-minute period has a binomial distribution.

Question 57

Which of the following about the binomial distribution is not a true statement?

A)The probability of success must be constant from trial to trial.
B)The random variable of interest is continuous.
C)Each outcome may be classified as either "success" or "failure".
D)Each outcome is independent of the other.

Question 58

NARRBEGIN: Unsafe Levels of Radioact
Unsafe Levels of Radioactivity
The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year.NARREND
{Unsafe Levels of Radioactivity Narrative} Find the probability that there will be no more than 1 incident in a year.

Question 59

The binomial probability distribution is a discrete probability distribution.

Question 60

If the probability of success p remains constant in a binomial distribution, an increase in n will not change the mean.

Question 61

The variance of a binomial distribution is equal to ____________________.

Question 62

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

A)Each trial results in two or more outcomes.
B)There is a sequence of identical trials.
C)The trials are independent of each other.
D)The probability of success p is the same from one trial to another.

Question 63

Evaluate the following binomial coefficients.
a.
b.
c.
d.

Question 64

If n = 10 and p = 0.60, then the mean of the binomial distribution is

A)0.06
B)2.65
C)6.00
D)5.76

Question 65

The variance of a binomial distribution for which n = 100 and p = 0.20 is:

A)100
B)80
C)20
D)16

Question 66

NARRBEGIN: Stress
Stress
Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed.NARREND
{Stress Narrative} Find the expected number of times a student may feel stressed during the final exam week.

Question 67

A binomial experiment consists of a(n) ____________________ number of trials, n.

Question 68

If n= 20 and p = 0.70, then the standard deviation of the binomial distribution is

A)0.14
B)2.05
C)14.0
D)14.7

Question 69

To find the probability that X is at most 10, you should find the probability that X is 10 or ____________________.

Question 70

NARRBEGIN: Stress
Stress
Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed.NARREND
{Stress Narrative} Find the probability distribution of X.

Question 71

The probability P(X $\le$ x) is called a(n) ____________________ probability. The binomial table reports these probabilities.

Question 72

The mean of a binomial distribution is equal to ____________________.

Question 73

NARRBEGIN: Stress
Stress
Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed.NARREND
{Stress Narrative} Find P(X < 3).

Question 74

NARRBEGIN: Stress
Stress
Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed.NARREND

-{Stress Narrative} Find P(2 $\le$ X $\le$ 4).

Question 75

The trials in a binomial experiment are ____________________, meaning the outcome of one trial does not affect the outcomes of any other trials.

Question 76

To find the probability that X is at least 10, you should find the probability that X is 10 or ____________________.

Question 77

The probability of a success in a binomial experiment is denoted by ____________________.

Question 78

The probability of a failure in a binomial experiment is denoted by ____________________.

Question 79

In each trial of a binomial experiment, there are ____________________ possible outcomes.

Question 80

The expected value, E(X), of a binomial probability distribution with n trials and probability p of success is:

A)n + p
B)np(1 - p)
C)np
D)n + p - 1