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?

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windyyork windyyork · Answer 1 · 2019-09-27T08:54:45+02:00

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.

Step-by-step 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 = [tex]\dfrac{507-65}{507}=\dfrac{442}{507}=0.87[/tex]

and the probability of failure is q = [tex]\dfrac{65}{507}=0.128[/tex]

Number of CDs selected = 3

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

[tex]P(X=3)=^3C_3(0.87)^3\\\\P(X=3)=0.658[/tex]

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.