Many companies use sampling to determine whether a batch should be accepted. An (n, c) sampling plan consists of inspecting n randomly chosen items from a batch and accepting the batch if c or fewer sampled items are defective. Suppose a company uses a (100, 5) sampling plan to determine whether a batch of 10,000 computer chips is acceptable.
a. The “producer’s risk” of a sampling plan is the probability that an acceptable batch will be rejected by the sampling plan. Suppose the customer considers a batch with 3% defectives acceptable. What is the producer’s risk for this sampling plan?
b. The “consumer’s risk” of a sampling plan is the probability that an unacceptable batch will be accepted by the sampling plan. Our customer says that a batch with 9% defectives is unacceptable. What is the consumer’s risk for this sampling plan?