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Consider an acceptance-sampling scheme in which factory takes delivery of a batch of components if random sample of 400 components contains fewer than M defectives. Otherwise the batch is returned tot he supplier. Suppose the factory manager wants to set M so that there is no more than a 10% risk of accepting a batch that has 5% or more defectives. Let P be the sample proportion of defectives. (In the following, use the approximate Normal distribution for P).

a) Suppose that the batch has 5% defectives. What is the value of c for which pr(p>c)=0.10? What value should M have?

b) Suppose the supplier makes a batch in which the true proportion of defectives is only 2%. If the cutoff in (a) is adopted, what is the probability that the batch will be sent back?

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