Suppose that whether or not a lot is good is random, that the long-run fraction of lots that are good is 95%, and that whether each lot is good is independent of whether any other lot or lots are good. Assume that the sample drawn from a lot is independent of whether the lot is good or bad. To simplify the problem even more, assume that good lots contain exactly 5 defective chips, and that bad lots contain exactly 20 defective chips. a. The expected number of lots the manufacturer must make to get one good lot that is not rejected by the test is ?
b. With this test and this mix of good and bad lots, among the lots that pass the test, the long-run fraction of lots that are actually bad is ?