Question

Asked Oct 14, 2019

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A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 52 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

The company will accept __ of the shipments and will reject __ of the shipments

Step 1

The probability that this whole shipment will be accepted is obtained below:

Here, the rates of defects is considered as a success, 5%, that is *p* = 0.05. The rates of not defects is considered as a failure, 95% (100% – 5%) of that is *q* = 0.95.

Therefore, the distribution is binomial distribution with sample size 52 and probability of success 0.05. That is, *X*~ Binomial (52, 0.05).

The formula for the probability of binomial distribution is,

Step 2

The required proba...

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