During a particular period a university's information technology office received 20 service orders for problems with printers, of which 8 were laser printers and 12 were inkjet models. A random sample of 5 of these service orders is to be selected for inclusion in a customer satisfaction survey. Let X = number of laser printers sampled. What is the distribution of X?

Question

Mathematics

Alyssa Ware

6 September, 11:09

During a particular period a university's information technology office received 20 service orders for problems with printers, of which 8 were laser printers and 12 were inkjet models. A random sample of 5 of these service orders is to be selected for inclusion in a customer satisfaction survey. Let X = number of laser printers sampled. What is the distribution of X?

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Walter Ashley · Answer 1

The distribution of X is Hyper-geometric distribution.

Step-by-step explanation:

A Hyper-geometric distribution is defined as the distribution of the exact number of success in a sample of size n taken from a population of size N.

The properties of a Hyper-geometric distribution are:

The sample is drawn from a population of finite size, N. Each participant, selected in a sample of size n, has only two outcomes, either a success or a failure. Each sample is selected without replacement.

In the provided case the random variable X is defined as the number of laser printers sampled.

The population consists of N = 20 printers of which 8 were laser printers and 12 were inkjet printers.

A sample of size, n = 5 is to be selected for inclusion in a customer satisfaction survey.

The success and failure can be defined as:

Success = A printer selected is a laser printer.

Failure = A printer selected is not a laser printer.

The random variable X satisfies all the properties of a Hyper-geometric distribution.

Thus, the distribution of X is Hyper-geometric distribution.