Math CentralQuandaries & Queries


Question from Katrina, a student:

The Medassist Pharmaceutical Company receives large shipments of aspirin tablets and uses this acceptance sampling plan: Randomly select and test 24 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?

Hi Katrina,

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 = 24. In the conventional language of binomial problems I am going to say that success is selecting a tablet that does not meet specifications. Thus if I randomly select one tablet then the probability of success is p = 0.04. Let X be the number of successes in the n trials, that is the number of tablets from the sample of 24 that don't meet specifications. The shipment is accepted if X= 0 or X = 1. Thus the question is to find

P(X = 0 or X = 1) = P(X = 0) + P(X = 1)

Use the expression for the binomial probability to calculate this probability.


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