Exam 6: Discrete Probability Distributions

The mean of a binomial distribution is the product of n and $\pi$ .

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. -This situation is an example of what type of discrete probability distribution?

To construct a binomial probability distribution,the number of trials and the probability of success must be known.

Which is true for a binomial distribution?

For a binomial distribution,the probability of a success stays the same for each trial,but the probability of a failure varies from trial to trial.

A mail-order house,advertising "same day" service,received a large number of complaints.A change in the handling of orders was made with less than 5 unfilled orders on hand (per picker)at the end of 95 out of every 100 working days.Frequent checks of unfilled orders at the end of the day revealed that the distribution of unfilled orders approximated a Poisson distribution;that is,most of the days there were no unfilled orders;some of the days there was one order,and so on.Since the average number of unfilled orders per picker was 2.0,the mail-order house lived up to its goal.

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

On a very hot summer day,5 percent of the production employees at Midland States Steel are absent from work.The production employees are randomly selected for a special in-depth study on absenteeism.What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?

Carlson Jewelers permits the return of their diamond wedding rings,provided the return occurs within two weeks of the purchase date.Their records reveal that 10 percent of the diamond wedding rings are returned.Five different customers buy five rings.What is the probability that none will be returned?

A Poisson distribution is a discrete probability distribution.It has the same four characteristics as the binomial,but in addition,the probability of a success is small and the number of trials is relatively large.

In a Poisson distribution the variance is equal to

For a binomial distribution,outcomes of an experiment are classified into one of two mutually exclusive categories (a success or a failure).

The binomial and Poisson distributions are discrete probability distributions.

For a binomial distribution,the data collected are the result of counts.

Which of the following is NOT a characteristic of a binomial probability distribution?

A probability distribution is a mutually exclusive and collectively exhaustive listing of experimental outcomes that can occur by chance and their corresponding probabilities.

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 mean of a probability distribution is called its expected value.

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

A new car was put into production.It involved many assembly tasks.Each car was inspected at the end of the assembly line and the number of defects per unit was recorded.For the first 100 cars produced,there were 40 defective cars.Some of the cars had no defects;a few had one defect,and so on.The distribution of defects followed a Poisson distribution.Based on the first 100 produced,about how many out of every 1,000 cars assembled should have one or more defects?