A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 4848 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 30003000 aspirin tablets actually has a 55% 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?

a) The probability that this whole shipment will be accepted is 30%.

b) Many of the shipments with this rate of defective aspirin tablets will be rejected.

Step-by-step explanation:

We have a shipment of 3000 aspirin tablets, with a 5% rate of defects.

We select a sample of size 48 and test for defectives.

If more than one aspirin is defective, the batch is rejected.

The amount of defective aspirin tablets X can be modeled as a binomial distribution random variable, with p=0.55 and n=48

We have to calculate the probabilities that X is equal or less than 1: P(X≤1).