Exam 5: Several Useful Discrete Distributions

Given that n is the number of trials of a random experiment, N is population size, M is the number of population units with the "success" characteristic, and p is the probability of success in the first trial, the mean of the hypergeometric random variable's probability distribution always equals:

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time or space is 1.5, then P(x = 2) is:

If the standard deviation for a Poisson distribution is known to be 3.60, the expected value of that Poisson distribution is:

Which of the following best describes a binomial probability distribution?

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.

About 80% of Florida residents believe that Florida is a nice or very nice place to live. Suppose that five randomly selected Florida residents are interviewed. Find the probability that all five residents think that Florida is a nice or very nice place to live. ______________ What is the probability that at least one resident does not think that Florida is a nice or very nice place to live? ______________ What is the probability that exactly one resident does not think that Florida is a nice or very nice place to live? ______________

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

Car color preferences change over the years and according to the particular model that the customer selects. In a recent year, 20% of all luxury cars sold were white. Assume that 25 cars of that year and type are randomly selected. Find the probabilities listed below: Define x to be the number of cars that are white. Then p = P(white) = 0.20 and n = 25. Use the cumulative binomial probabilities table in Appendix I of your book. At least five cars are white. ______________ At most six cars are white. ______________ Exactly four cars are white. ______________ More than three cars are white. ______________ Between three and five cars (inclusive) are white. ______________ More than 20 cars are not white. ______________

The quality of computer disks is measured by sending the disks through a certifier which counts the number of missing pulses. A certain brand of computer disks averages 0.1 missing pulse per disk. Let the random variable x denote the number of missing pulses. What is the distribution of x? Type of distribution: ______________ Mean of distribution: ______________ Find the probability the next inspected disk will have no missing pulse. ______________ Find the probability the next disk inspected will have more than one missing pulse. ______________ Find the probability neither of the next two disks inspected will contain any missing pulse. ______________

A package of six light bulbs contains 2 defective bulbs. If three bulbs are selected for use, find the probability none are defective. ______________

The Poisson parameter is the mean number of occurrences of an event per unit of time or space during the Poisson process.

A salesperson has found the probability of making a sale on a particular product manufactured by his or her company is 0.05. If the salesperson contacts 140 potential customers, what is the probability he or she will sell at least 2 of these products? ______________

Which of the following experiments can be modeled by the Poisson distribution?

A fellow student tells you he is working with a discrete random variable, x, which takes on integer values from 0 to 50 and has a mean of 40 and a variance of 10. Is x a binomial random variable? ______________ Explain. ________________________________________________________

Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

It was estimated that 2% of a particular 1997 model minivan had incorrectly installed brake lines. Suppose 300 minivans of this model are selected at random. Let x represent number of minivans with incorrectly installed brake lines. What is the probability that 9 have incorrectly installed brake lines? ______________

Which of the following best describes the binomial probability distribution?

For a binomial experiment with n trials, p is the probability of success, q is the probability of failure, and x is the number of successes in n trials. Which one of the following statements is correct?

The number of defects in a random sample of 200 parts produced by a machine is binomially distributed with p = .03. Based on this information, the standard deviation of the number of defects in the sample is 5.82.

If the random variable x is binomially distributed with n = 10 and p = .05, then P(x = 2) is: