The company will accept what % of the shipments and will reject what % of the sh

Question

The company will accept what % of the shipments and will reject what % of the shipments, Will almost all such shipments be accepted, or will many be rejected?

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 4000 aspirin tablets actually has a 4% 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 (Round to four decimal places as needed.)

Explanation / Answer

Ans:

Binomial distribution:

probability of being defective in a shipment=0.04

P(k<=1)=47C0*(0.04)0*(0.96)47+47C1*(0.04)1*(0.96)46

=0.1468+0.2875

=0.4343

Probability of accepting the shipment=0.4343

43.43% of the shipments will be accepted and 56.57% will be rejected.

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