5.91 Sampling for defectives from large lots of a manufactured product yields a number of defectives Y that follows a binomial probability distribution.

A sampling plan involves specifying the number of items to be included in a sample n and an acceptance number

a. The lot is accepted if Y a and rejected if Y a. Let p denote the proportion of defectives in the lot. For n  5 and a  0, calculate the probability of lot acceptance if a p  0 b p  0.1 c p  0.3 d p  0.5 e p  1.0 A graph showing the probability of lot acceptance as a function of lot fraction defective is called the operating characteristic curve for the sample plan. Construct this curve for the plan n  5, a  0. Note that a sampling plan is an example of statistical inference. Accepting or rejecting a lot based on information contained in the sample is equivalent to concluding that the lot is either “good” or “bad”, respectively. “Good”

implies that a low fraction is defective and that the lot is therefore suitable for shipment.