Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of n components can be viewed as the n trials of a binomial experiment. The outcome for each component tested (trial) will be that the component is classified as good or defective. Reynolds Electronics accepts a lot from a particular supplier if the defective components in the lot do not exceed 1%. Suppose a random sample of five items from a recent shipment is tested.
a. Assume that 1% of the shipment is defective. Compute the probability that no items in the sample are defective.
b. Assume that 1% of the shipment is defective. Compute the probability that exactly one item in the sample is defective.
c. What is the probability of observing one or more defective items in the sample if 1% of the shipment is defective?
d. Would you feel comfortable accepting the shipment if one item was found to be defective? Why or why not?