Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 59 tablets, then accept th batch if there is only one or none that doesn't meet the required specifications. If one shipment of 4000 aspirin tablets actually has a 4% rate of defects, what 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 (Round to four decimal places as needed.)

Answer 1

We have a total number of 4000 tablets in a shipment. 59 out of these 4000 need to be randomly selected for sampling.

The number of actual defected tablets is 0.04*4000 = 160

The number of tablets that are acceptable are 3840

We need to find the probability that the whole shipment is accepted given that atmost one of the tablets in the sample of 59 is defected.

The given probability can be calculated as:

$P(accept-shipment)=\frac{_{59}^{3840}\textrm{C}+_{58}^{3840}\textrm{C}*_{1}^{160}\textrm{C}}{_{59}^{4000}\textrm{C}}$

Hence the required probability is 0.3089 or 30.89%

P.S.: We can only answer one question at a time. Kindly post the rest of the questions as separate questions.