Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 36 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 5000 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?

Answer 1

The probability that this whole shipment will be​ accepted is 0.8382. Almost all such shipments be​ accepted as the probability of accepting is higher.

Explanation:

Consider the provided information.

The probability for accepting the whole batch if there is only one or none that​ doesn't meet the required specifications.

Aspirin tablets actually has a 2​% rate of​ defects. Thus, the rate of aspirin tablets are not defected 98%.

Which can be written as:

P(x=0 or x=1)

P(no defects out of 36)=
`^(36)c_0 * (0.02)^0 * (0.98)^(36)`

P(no defects out of 36)=
`0.483213128206`

P(one defects out of 36)=
`^(36)c_1 * (0.02)^1 * (0.98)^(35)`

P(one defects out of 36)=
`36 * 0.02 * (0.49307)`

P(one defects out of 36)=
`0.3550104`

The probability that the whole shipment will accepted is the sum of the individual probabilities which is:

0.4832+0.3550=0.8382

Hence, the probability that this whole shipment will be​ accepted is 0.8382. Almost all such shipments be​ accepted as the probability of accepting is higher.