A pharmaceutical company receives large shipments of aspirin tablets. The accept

Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is randomly select and test 18 tablets, then accept the whole batch if there is only one or nine that doesn’t meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has 5% rate of defects what is the probability that this whole shipment will be accepted? A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is randomly select and test 18 tablets, then accept the whole batch if there is only one or nine that doesn’t meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has 5% rate of defects what is the probability that this whole shipment will be accepted?

Explanation / Answer

Number of tablets to be tested = 18

We will accept the whole batch if there is only one or none that doesn’t meet the required specifications.

Here, Pr(defective rate) = 0.05

so, the shipment will be accepted when

Pr(X 1) = BINOMIAL (X 1 ; 18 ; 0.05) = BINOMIAL (X = 0 ; 18 ; 0.05) + BINOMIAL(X = 1 ; 18 ; 0.05)

= 18C0 (0.05)0(0.95)18 + 18C1 (0.05)1 (0.95)17

= 0.7735

so the probability that shipment will be accepted = 0.7735

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