The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that meets the contract requirements will be shipped without further inspection is approximately .9139.

Question

Quizplus · Accepted Answer

Given that 5% of the items can be defective according to contract specifications, the probability of finding 0 or 1 defective item in a sample of 10 can be calculated using the binomial distribution formula. The probability of a batch meeting the contract requirements (i.e., having 5% defective items) and being shipped without further inspection (finding 0 or 1 defective item in the sample) is indeed approximately 0.9139. This calculation is based on the binomial probability formula, considering the success probability (p = 0.05 for a defective item) and the sample size (n = 10).

The Hawkins Company Randomly Samples 10 Items from Every Large