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 967 CDs, and 88 are defective. If 3 of these CDs are randomly selcted 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 ____

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.​Yes, because if all three CDs in the sample are good then the entire batch must be good.

C.​No, because only a probability of 1 would indicate the entire batch consists of good CDs.

D.No, because the sample will always consist of good CDs.

Answer 1

(a)

Population:
Defective = 88

Non-defective = 879

Total items = 967

Sample
Defective = 0

Non-defective = 3

Total items = 3

Number of ways of selecting 3 items from 967 items = 967C3 = 1502377955

Number of ways of selecting 3 non-defectives from 879 non-defectives = 879C3 = 112805879

So,

The probability that the whole batch is accepted is = 112805879/ 1502377955

                                                                          = 0.0750

So,

Answer is:

0.0750

(b)

Correct option:

C.​No, because only a probability of 1 would indicate the entire batch consists of good CDs