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 47 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is ?

Explanation / Answer

n= 47, p = 0.03 ,q=0.97

P( acceptance) = P( 0 or 1 defects in 47 tests) = 47C0 * 0.97^47 + 47C1* 0.03*0.97^46 =  1* 0.97^47 + 47* 0.03*0.97^46 = 0.5862

he probability that this whole shipment will be accepted is 0.5862

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