Question

In a food production process, packaged items are sampled as they come off a production line, a random sample of 5 items from each production batch is checked to see if each is tightly parked. A batch is accepted if all 5 sample items are satisfactory, and rejected if there are 3 or more unsatisfactory packages in it; otherwise a further sample is taken before making a decision. If in fact the packing machine is giving 80% of items properly parked, what is the probability that this second sample will be necessary? The second sample also consists of 5 items. What is the probability that, out of the two samples (10 items), there are 9 satisfactory? What are the assumptions behind your calculations?

Answer 1