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

Explanation / Answer

Here it is given that lot will be accepted if atleast 9 out of 10 are good

Further probability of defect is 0.02, hence probability of good is 1-0.02=0.98

So we need to find P(x>=9)

i.e P(10)+P(9)

P(10)=0.98^10=0.8171

P(9)=10*0.02*0.98^9=0.1667

Hence required probability is 0.8171+0.1667=0.9838

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