Question

A company is interested in evaluating its current inspection procedure on large shipments of identical items. The procedure is to take a sample of 5 items and pass the shipment if no more than 1 item is found to be defective. It is known that items are defective at a 10% rate overall.

What is the probability that the inspection procedure will pass the shipment?

Answer 1

0.91854

Explanation:

Given that a company is interested in evaluating its current inspection procedure on large shipments of identical items.

The procedure is to take a sample of 5 items and pass the shipment if no more than 1 item is found to be defective.

It is known that items are defective at a 10% rate overall.

If X is the number of defectives in the sample of 5, we find that X has two outcomes and each trial is independent of the other

So X is binomial with n =5, and p = 0.10

the probability that the inspection procedure will pass the shipment

=
`P(X\leq 1)\\ \\= (0.9)^5 + 5 (0.1)(0.9)^4\\= (0.9^4) (0.9+0.5)\\= 0.91854`