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

1881​CDs, and 104are 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?

Answer 1

So the probability that the entire batch is accepted = The Probability that the 104 defected CDs are not among the chosen 3 CDs .

So the total number of non- defective CDs = 1881-104 = 1777

So the required probability = (1777/1881)*(1776/1880)*(1775/1879)

= 0.843.

So we can conclude that there is a probability of 0.843 , that the batch will be accepted.

But this outcome does not suggest that the entire batch consists of good CDs. This is so because all the CDs of this batch are not checked and the decision of acceptance is taken only by checking 3 CDs out of 1881 CDs.