Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 60 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 2% 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 probability that this whole shipment will be accepted is _____.

Answer #1

Let X be a random variable which denotes the number of aspirin tablets that doesn't meet the required specifications (in a sample of 60 tablets)

The chances of an aspirin tablet being defective is independent of any other tablet.

Thus, X follows binomial distribution where

n = 60, p = 0.02

The probability that the shipment will be accepted = P(X ≤ 1)

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

= (1-0.02)^{48} +
^{48}C_{1}*0.02*(1-0.02)^{47}

= **0.751**

There is only a 75.1% chance that such shipment will be accepted.

Thus, it can be concluded that many of such shipments will be rejected

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41
tablets, then accept the whole batch if there is
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specifications. If one shipment of
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%
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