Question 1076846: With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. A company has just manufactured 1282 CDs, and 466
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?
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! 466/1282=0.3635 probability one is defective
0.6365, probability one is not defective
0.6365^3, probability three are not defective if independent or 0.2579.
With such a high probability of one's being defective, checking three is not too helpful. The above shows that there is a 1 in 4 chance of accepting the whole batch with 1/3 defective. The likelihood of the whole batch being good is 0.6365^1282, which is, on a calculator, 0.
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