Acceptance Sampling?

Question

a pharmaceutical company receives large shipments of aspirin tablets. the acceptance sampling plan is to randomly select and test 14 tablets, then accept the whole batch if there is only one or none that doesnt meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted?

Answer 1

In order for there to be no defects then all 14 of the test tablets must be good so 

 

P(no defects out of 14) = 0.97¹⁴ ~ 0.6528  

 

If there is 1 tablet that is bad then it can be any one of the 14 tablets (this can happen in 14 different ways), times the probability that 1 tablet is bad and 13 are good, so 

 

P(1 defect out of 14) = 14*0.03*0.97¹³ ~ 0.2827

 

The probability that either of these cases happen is the sum of the individual probabilities which is 

 

P(shipment accepted) = 0.6528 + 0.2827 = 0.9355