Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 57 ​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 5​% 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

This question is to be solved with a binomial distribution.

The binominal distribution formula is given by

where n the total number of trails
x is the number of successes out of n trials
p is the probability of success
q is the probability of failure

We need to find the

In this case we have

n = 57 (No. of sample)
p = 0.05 ( Probability of getting a defective sample)
q = 0.95

the probability that this whole shipment will be​ accepted is 0.2149