Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 58 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 3% 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?

Round to four decimal places as needed

Answer 1

Here we have

$N=3000,n=58,p=0.03$

Let X is a random variable shows the number of defective aspirin tablets in the sample. Since population is very large from sample size, that is so we can use binomial distribution. That is X has binomial distribution with parameters n=58 and p=0.03.

N20n

The probability that shipment will be accepted is:

1(58 P(X 1) = > ( ) (0.03)"(1-0.03)58-r-0.4775

Answer: 0.4775

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That is the company will accept 47.75% of the shipments and will reject 52.25% of the shipment so many of the shipment will be rejected.