A pharmaceutical company receives large shipments of aspirin

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 21 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted?

The probability that this whole shipment will be accepted is ____.

Solution

Probability that a randomly picked up tablet is unacceptable = 0.03
=> probability that the shipment may be accepted
= probability that all 21 tablets of the sample are acceptable or 1 is acceptable
= (0.97)^21 + 21C1 * (0.97)^14 * (0.03)
=  0.8