A manufacturer of computer memory chips produces chips in lotsof 1000. If nothing has gone wrong in the manufacturing process, atmost 5 chips each lot would be defective, but if something does gowrong, there could be far more defective chips. If something goeswrong with a given lot, they discard the entire lot. It would beprohibitively expensive to test every chip in every lot, so theywant to make the decision of whether or not to discard a given loton the basis of the number of defective chips in a simple randomsample. They decide they can afford to test 100 chips from eachlot. You are hired as their statistician.
There is a tradeoff between the cost of eroneously discarding agood lot, and the cost of warranty claims if a bad lot is sold. Thenext few problems refer to this scenario.
(Continues previous problem.) Suppose that whether or not a lotis good is random, that the long-run fraction of lots that are goodis 97%, and that whether each lot is good is independent of whetherany other lot or lots are good. Assume that the sample drawn from alot is independent of whether the lot is good or bad. To simplifythe problem even more, assume that good lots contain exactly 5defective chips, and that bad lots contain exactly 20 defectivechips.
Problem 16
(Continues previous problem.) The expected number of lots themanufacturer must make to get one good lot that is not rejected bythe test is (Q22)
Problem 17
(Continues previous problem.) With this test and this mix ofgood and bad lots, among the lots that pass the test, the long-runfraction of lots that are actually bad is(Q23)
