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 1034 ​CDs, and 68 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

Answer 1

If 3 of the 1034 CDs are randomly selected for​ testing, then the probability of the whole batch being selected is

This is because a batch will be accepted if we choose 3 CD's from the non-defective portion which are 966 out of 1034.

Acceptance of the batch does not suggest that the batch consists of only good CD's because we are inspecting only 3 out of 1034 CD's. A batch cannot be said to have all good CD's unless the whole batch has not been inspected.