The Ziteck Corporation buys parts from international suppliers. One part is currently being purchased from a Malaysian supplier under a contract that calls for at most 5% of the 10,000 parts to be defective. When a shipment arrives, Ziteck randomly samples 10 parts. If it finds 2 or fewer defectives in the sample, it keeps the shipment; otherwise, it returns the entire shipment to the supplier.
a. Assuming that the conditions for the binomial distribution are satisfied, what is the probability that the sample will lead Ziteck to keep the shipment if the defect rate is actually 0.05?
b. Suppose the supplier is actually sending Ziteck 10% defects. What is the probability that the sample will lead Ziteck to accept the shipment anyway?
c. Comment on this sampling plan (sample size and accept/reject point). Do you think it favors either Ziteck or the supplier? Discuss.