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 + ⁴⁸C₁*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