A manufacture receives a lot of 100 parts from a vendor. The lot will be unacceptable if more than five of the parts are defective. The manufacturer is going to select randomly K parts from the lot for inspection and the lot will be accepted if no defective parts are found in the sample.

(a)How large does K have to be to ensure that the probability that the manufacturer accepts and unacceptable lot is less than 0.1?

(b)Suppose the manufacturer decides to accept the lot if there is at most one defective in the sample. How large does K have to be to ensure that the probability that the manufacturer accepts an unacceptable lot is less than 0.1?