question in description

Question

A pharmaceutical company receives large shipments of ibuprofen tablets and uses this acceptance sampling plan: randomly select and test 27 tablets, then accept the whole batch if there is at most one that doesn’t meet the required specifications. If a particular shipment of thousands of ibuprofen tablets actually has a 12% rate of defects, what is the probability that this whole shipment will be accepted?

Answer 1

Pr(accept) = Pr(1 failed tablet out of 27 sample) + Pr(no failed tablet in 27 sample)

= C(27,1) * (1-12%)²⁶ * (12%) + (1-12%)²⁷

= 0.1167 + 0.0317

= 0.1484 = 14.84%