Exam 6: Discrete Probability Distributions

The following is a Poisson probability distribution with µ = 0.1. The variance of the distribution is

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station. What is the probability that at least ten pay in cash?

The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsightly blemishes often appear because of improper mixture or other problems. A worker counted the number of blemishes on each door. Most doors had no blemishes; a few had one; a very few had two, and so on. The average number was 0.5 per door. The distribution of blemishes followed the Poisson distribution. Out of 10,000 doors painted, about how many would have no blemishes?

For the following probability distribution, The variance is _____________.

A tennis match requires that a player win three of five sets to win the match. If a player wins the first two sets, what is the probability that the player wins the match, assuming that each player is equally likely to win each match?

For the following distribution, What is the variance of the distribution?

When observing a check-out line at a food store, the average number of people served is 30 per hour. Using the Poisson distribution, what is the probability that no (zero) people check out in any given hour?

For the following distribution, What is the mean of the distribution?

Which is true for a binomial distribution?

How many experimental outcomes are possible for the Binomial distribution? _______

A _______________ random variable can assume only a certain number of separated values.

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have no messages?

The following is a binomial probability distribution with n = 3 and $\pi$ = 0.20. The mean of the distribution is

When observing a check-out line at a food store, the average number of people served is 15 per hour. Using the Poisson distribution, what is the standard deviation of the number of people served in an hour?

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the standard deviation of the number of days absent?

For the following probability distribution, The mean is _____________.

Elly's hot dog emporium is famous for its chilidogs. Elly's latest sales indicate that 30% of the customers order their chilidogs with hot peppers. Suppose 18 customers are selected at random. What is the probability that fifteen or more customers will want hot peppers? ____________

The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period? ______

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages?

The variance of a binomial distribution is found by n $\pi$ (1 - $\pi$ ).