Question

A pharmaceutical company receives large shipments of aspirin tabletsThe acceptance sampling plan is to randomly select and test 53 tablets, then accept the whole batch if there is only one of the required specifications. one shipment of 3000 aspirin tablets has a 5% rate of defectswhat is the probability that this whole shipment will be accepted? almost all such shipments be accepted, or will many be rejected?

Answer 1

The acceptance sampling plan for the pharmaceutical company is to randomly select and test 53 tablets from each shipment, accepting the whole batch if there is only one defect. The probability of accepting the whole shipment can be calculated using binomial probability.

Step-by-step explanation:

The acceptance sampling plan for the pharmaceutical company is to randomly select and test 53 tablets from each shipment. The whole batch will be accepted if there is only one tablet that doesn't meet the required specifications.

In this case, the shipment has a 5% rate of defects, so the probability of accepting the whole shipment can be calculated using binomial probability.

The probability of exactly one defect in a sample of 53 tablets can be calculated using the binomial probability formula:

P(X = 1) = C(53, 1) * (0.05)^1 * (0.95)^52

where C(53, 1) is the number of ways to choose 1 tablet out of 53.

Calculating this probability will give you the probability of accepting the whole shipment.