Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 16 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 2% rate of​ defects, what is the probability that this whole shipment will be​ accepted?

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

​(Round to three decimal places as​ needed.)

Answer 1

In order for there to be no defects then all 16 of the test tablets must be good so

P(no defects out of 16) = 0.98¹⁶ = 0.7238

If there is 1 tablet that is bad then it can be any one of the 16 tablets (this can happen in 16 different ways), times the probability that 1 tablet is bad and 15 are good, so

P(1 defect out of 16) = (16)*(0.02)*(0.98¹⁵) = 0.2363

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

P(shipment accepted) = 0.7238 + 0.2363 = 0.960

The probability that this whole shipment will

be accepted is 0.960