Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptence sampling plan is to randomly select and test 23 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 3.0% rate of defects, what is the probability that this whole shipment will be accepted? (round to three decimal places as needed)

Answer 1

This is a binomial distribution problem or sometimes called repeated independent trials. You have a very large shipment of tablets and you are to randomly select n = 23. In the conventional language of binomial problems we are going to say that success is selecting a tablet that does not meet specifications. Thus if we randomly select one tablet then the probability of success is p= 0.03. Let X be the number of successes in the n trials that is the number of tablets from the sample of 23 that don't meet specifications. The shipment is accepted if X = 0 or X=1 or X = 2.

Thus the question is to find

P(X=0)=0.4963064

P(X=1)= 0.3530427

P(X=2)=0.1201073

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