A pharmaceutical company receives large shipments of aspirin tablets. The accept

Question

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

2424

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

44 %

rate of defects, what is the probability that this whole shipment will be accepted?

The probability that this whole shipment will be accepted is

Round to three decimal places as needed.

Explanation / Answer

Solution:

In order for there to be no defects then all 24 of the test tablets must be good so

P(no defects out of 24) = 0.9624 ~ 0.3754

If there is 1 tablet that is bad then it can be any one of the 24 tablets (this can happen in 24 different ways), times the probability that 1 tablet is bad and 23 are good, so

P(1 defect out of 24) = 24*0.04*0.9723 ~ 0.4765

The probability that either of these cases happen is the sum of the individual probabilities which is

P(shipment accepted) = 0.3754 + 0.4765 = 0.8519

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