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 is accepted if every item in the sample is okay. A company has just manufactured 1362 CDs, and 448 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?

Does the result in (a) suggest that the entire batch consists of good CDs? Why or why not?

A. Yes, because it is not unlikely that the batch will be accepted.
B.No, because the sample will always consist of good CDs.
C.Yes, because if all three CDs in the sample are good then the entire batch must be good.
D.No, because only a probability of 1 would indicate the entire batch consists of good CDs.

Explanation / Answer

The probability that a CD is not defective is:

1-(448/1362)

=0.67

If 3 of these CDs are randomly selected for testing, then the probability that the entire batch will be accepted is:

1362C3*0.67^3(1-0.67)^(1362-3)

=<0.000001

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