Deck 7: B: Random Variables and Discrete Probability Distributions

Question 1

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

Answer 1

True

Question 2

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

Answer 2

C

Question 3

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.

Answer 3

C

Question 4

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

Question 5

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

Question 6

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

Question 7

The Poisson probability distribution is a continuous probability distribution.

Question 8

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

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 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 11

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 12

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

Question 13

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

Question 14

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 15

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

Question 16

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

Question 17

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 18

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

Question 19

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 20

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 21

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

Question 22

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 23

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

Question 24

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 25

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

Question 26

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 27

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

Question 28

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

Question 29

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 30

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

Question 31

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

Question 32

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 33

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 34

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 35

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 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.
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 37

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 38

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 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 13 calls between 2 and 4 P.M.on a particular afternoon.

Question 40

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

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 variance of the number of incidents in one year.

Question 42

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 43

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 44

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.