A quality-control inspector is testing a batch of printed circuit boards to see whether they are capable of performing in a high temperature environment. He knows that the boards that will survive will pass all five of the tests with probability 98%. They will pass at least four tests with probability 99%, and they always pass at least three. On the other hand, the boards that will not survive sometimes pass the tests as well. In fact, 3% pass all five tests, and another 20% pass exactly four. The rest pass at most three tests. The inspector decides that if a board passes all five tests, he will classify it as “good.” Otherwise, he’ll classify it as “bad.”

(a) What does a type I error mean in this context?

(b) What is the probability of a type I error?

(c) What does a type II error mean here?

(d) What is the probability of a type II error?