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 507 ​CDs, and 65 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 1

Answer: Probability that the entire batch will be accepted is 0.658.

Yes, this suggests entire batch of good CDs as it is the only condition to get accepted.

Explanation:

Since we have given that

Number of CDs = 507

Number of defective = 65

Since the entire batch will be accepted.

So, the probability of success is p =
`(507-65)/(507)=(442)/(507)=0.87`

and the probability of failure is q =
`(65)/(507)=0.128`

Number of CDs selected = 3

So, Probability that the entire batch will be accepted is given by

`P(X=3)=^3C_3(0.87)^3\\\\P(X=3)=0.658`

Hence, Probability that the entire batch will be accepted is 0.658.

Yes, this suggests entire batch of good CDs as it is the only condition to get accepted.