With one method of a procedure called acceptance sampling, a sample of items is

Question

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch accepted if every item in the sample is okay. A company has just manufactured 1636 CDs. and 665 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted? Does this outcome suggest that the entire batch consists of good CDs? Why or why not? If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted? The probability that the whole batch is accepted is

Explanation / Answer

As it has been given information about acceptance sampling we know that is a major component of quality control and is useful when the cost of testing is high compared to the cost of passing a defective item or when testing is destructive. It is a compromise between doing 100% inspection and no inspection at all.

Sampling scheme used here is without replacement scheme.

We are selecting the entire lot of CD if every item of the sample is ok. That is, we are doing an 100% inspection in our survey.

No. of manufactured CDs=1536

Defective CDs=665

Selected Cds from random allocation (n)=3

Prob( Entire batch is accepted)=

prob( none of the Cd is defective)= 0.17

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