A firm receives components from a supplier in large batches, for use in its production process. Production is uneconomic if a batch containing 10% or more defective components is used. The firm checks the quality of each incoming batch by taking a sample of 15 and rejecting the whole batch if more than one defective component is found.

(a) If a batch containing 10% defectives is delivered, what is the probability of its being accepted?

(b) How could the firm reduce this probability of erroneously accepting bad batches?

(c) If the supplier produces a batch with 3% defective, what is the probability of the firm sending back the batch?

(d) What role does the assumption of a ‘large’ batch play in the calculation?