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 to randomly select and test 12 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 5.0% rate of defects, what is the probability that this whole shipment will be accepted?

The probability that this whole shipment will be accepted is ? (Round to three decimal places as needed.)

Explanation / Answer

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 12 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications.

a particular shipment of thousands of aspirin tablets actually has a 5.0% rate of defects

let X be the random variable denoting the number of defective aspirin tables in 12 tablets

so X~Bin(12,0.05)

so the pmf of X is P[X=x]=12Cx(0.05)x(1-0.05)12-x       x=0,1,2,......,12

The entire shipment is accepted if at most 2 tablets do not meet the required specifications

so the probability that this whole shipment will be accepted is

P[X<=2]=P[X=0]+P[X=1]+P[X=2]

            =12C0(0.05)0(1-0.05)12-0 +12C1(0.05)1(1-0.05)12-1 +12C2(0.05)2(1-0.05)12-2

                 =0.540+0.341+0.099=0.980    [rounded to three decimal] [answer]

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