Comparing sampling plans: a very large batch of drug tablets has arrived at a distributor. The batch can be characterized as "acceptable" only if the proportion of defective tablets is at most 10%. The distributor decides to randomly select 10 tablets and to accept the batch only if the number of defective tablets in the sample is at most 2.

a)What is the probability that the batch will be accepted when the actual proportion of defectives is 1%? 5%? 10%? 25%?

b)Let denote that actual proportion of defectives in the batch. Plot a graph with the probability of accepting the batch, , on the vertical axis, and on the horizontal axis, with 0 ? ? 1.

c)Repeat parts a) and b) if the batch is accepted when the number of defective tablets in the sample is at most 1 instead of 2.

d)Repeat parts a) and b) if we increase the sample size from 10 to 15 tablets. A batch is still accepted when the number of defective tablets in the sample is at most 2.

e)Which of the three sampling plans, that of part a), c), or d), appears most satisfactory, and why?

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