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StatisticsQ&A LibraryA pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 16 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?Question

Asked Oct 16, 2019

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*A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 16 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?*

Step 1

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

Here, the rates of defects is considered as a success, 4%, that is *p* = 0.04. The rates of not defects is considered as a failure, 96% (100% – 4%) of that is *q* = 0.96.

Therefore, the distribution is binomial distribution with sample size 16 and probability of success 0.04. That is, *X*~ Binomial (16, 0.04).

The formula for the probability of binomial distribution is,

Step 2

The required proba...

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