Deck 7: Random Variables and Discrete Probability Distributions

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

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 6

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 7

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 8

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 9

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 10

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

Question 11

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 12

The Poisson probability distribution is a continuous probability distribution.

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

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 15

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 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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 23

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.

-{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 24

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

Question 25

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

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

Question 26

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

Question 27

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 28

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

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

Question 29

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

Question 30

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 31

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

Question 32

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.

-{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 possible values of a Poisson random variable start at ____________________.

Question 34

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

Question 35

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

-{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 36

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.

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

Question 37

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.

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

Question 38

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.

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

Question 39

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.

-{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 40

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

Question 41

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.
{Unsafe Levels of Radioactivity Narrative} Find the probability that there will be at least 3 incidents in a year.

Question 42

The time required to drive from New York to New Mexico is a discrete random variable.

Question 43

The number of home insurance policy holders is an example of a discrete random variable

Question 44

The amount of milk consumed by a baby in a day is an example of a discrete random variable.

Question 45

Given that X is a discrete random variable, then the laws of expected value and variance can be applied to show that E(X + 5) = E(X) + 5, and V(X + 5) = V(X) + 25.

Question 46

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.
{Unsafe Levels of Radioactivity Narrative} Find the probability that there will be no more than 1 incident in a year.

Question 47

Faculty rank (professor, associate professor, assistant professor, and lecturer) is an example of a discrete random variable.

Question 48

The number of homeless people in Boston is an example of a discrete random variable.

Question 49

Another name for the mean of a probability distribution is its expected value.

Question 50

The length of time for which an apartment in a large complex remains vacant is a discrete random variable.

Question 51

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.
{Unsafe Levels of Radioactivity Narrative} Find the variance of the number of incidents in one year.

Question 52

A table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities, is referred to as probability distribution.

Question 53

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 54

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.
{Unsafe Levels of Radioactivity Narrative} Find the probability that there will be exactly 3 incidents in a year.

Question 55

The mean of a discrete probability distribution for X is the sum of all possible values of X, divided by the number of possible values of X.

Question 56

A continuous variable may take on any value within its relevant range even though the measurement device may not be precise enough to record it.

Question 57

A random variable is a function or rule that assigns a number to each outcome of an experiment.

Question 58

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.
{Unsafe Levels of Radioactivity Narrative} Find the standard deviation of the number of incidents is in one year.

Question 59

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.
{Unsafe Levels of Radioactiviy Narrative} Find the probability that there will be at least 1 incident in a year.

Question 60

For a random variable X, if V(cX) = 4V(X), where V refers to the variance, then c must be 2.

Question 61

Which of the following are required conditions for the distribution of a discrete random variable X that can assume values x_i?

A) 0 $\le$ p(x_i) $\le$ 1 for all x_i
B)
C) Both a and b are required conditions.
D) Neither a nor b are required conditions.

Question 62

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance.How long a person has been a licensed rider is an example of a(n) ____________________ random variable.

Question 63

The dean of students conducted a survey on campus.Grade point average (GPA) is an example of a(n) ____________________ random variable.

Question 64

Which of the following is not a required condition for the distribution of a discrete random variable X that can assume values x_i?

A) 0 $\le$ p(x_i) $\le$ 1 for all x_i
B)
C) p(x_i) > 1 for all x_i
D) All of these choices are true.

Question 65

An auto insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance.A person's age is an example of a(n) ____________________ random variable.

Question 66

For a random variable X, V(X + 3) = V(X + 6), where V refers to the variance.

Question 67

In the notation below, X is the random variable, c is a constant, and V refers to the variance.Which of the following laws of variance is not true?

A) V(c) = 0
B) V(X + c) = V(X) + c
C) V(cX) = c² V(X)
D) None of these choices.

Question 68

For a random variable X, E(X + 2) - 5 = E(X) - 3, where E refers to the expected value.

Question 69

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance.The distance a person rides in a year is an example of a(n) ____________________ random variable.

Question 70

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance.The number of tickets a person has received in the last 3 years is an example of a(n) ____________________ random variable.

Question 71

Which of the following is a continuous random variable?

A) The number of employees of an automobile company.
B) The amount of milk produced by a cow in one 24-hour period.
C) The number of gallons of milk sold at Albertson's grocery store last week.
D) None of these choices.

Question 72

The number of accidents that occur annually on a busy stretch of highway is an example of:

A) a discrete random variable.
B) a continuous random variable.
C) expected value of a discrete random variable.
D) expected value of a continuous random variable.

Question 73

The amount of time that a microcomputer is used per week is an example of a(n) ____________________ random variable.

Question 74

A table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities, is called a(n):

A) probability distribution.
B) discrete random variable.
C) expected value of a discrete random variable.
D) None of these choices.

Question 75

A function or rule that assigns a numerical value to each outcome of an experiment is called:

A) a sample space.
B) a probability distribution.
C) a random variable.
D) None of these choices.

Question 76

The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:

A) variance.
B) standard deviation.
C) expected value.
D) None of these choices.

Question 77

A lab at the DeBakey Institute orders 150 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Suppose the mean cost of rats used in lab experiments turned out to be $20.00 per week.Interpret this value.

A) Most of the weeks resulted in rat costs of $20.00
B) The median cost for the distribution of rat costs is $20.00
C) The expected or average costs for all weekly rat purchases is $20.00
D) The rat cost that occurs more often than any other is $20.00

Question 78

An auto insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance.The number of claims a person has made in the last 3 years is an example of a(n) ____________________ random variable.

Question 79

In the notation below, X is the random variable, E and V refer to the expected value and variance, respectively.Which of the following is false?

A) E(3X) = 3E(X)
B) V(2) = 0
C) E(X + 1) = E(X) + 1
D) All of these choices are true.

Question 80

Which of the following is a discrete random variable?

A) The Dow Jones Industrial average.
B) The volume of water in Michigan Lakes.
C) The time it takes you to drive to school.
D) The number of employees of a soft drink company.