Q1. 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% defectives in the lot. 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 reject the shipment if the defect rate is actually 0.05? Show work.
b) Suppose the supplier is actually sending Ziteck 10% defectives. What is the probability that the sample will lead Ziteck to accept the shipment anyway? Show work.
c) Comment in detail on this sampling plan (sample size and accept/reject point). Do you think it favors either Ziteck or the supplier? Give reason for your answer. (100-200 words). General answers are not expected.
Q2. Two automatic dispensing machines are being considered for use in a fast-food chain. The first dispenses an amount of liquid that has a normal distribution with a mean of 11.9 ounces and a standard deviation of 0.07 ounces. The second dispenses an amount of liquid that has a normal distribution with a mean of 12.0 ounces and a standard deviation of 0.05 ounces. Acceptable amounts of dispensed liquid are between 11.9 and 12.0 ounces. Calculate the relevant probabilities and determine which machine should be selected. Note: Show all the steps.