With one method of a procedure called acceptance sampling. a sample of items is

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 simple it okay A company hat just manufactured 1463 CDs, and 150 are defective If 3 of these CDs are randomly selected for testing, what is the probability that the entire hatch 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 foe testing, what is the probability that the entire batch will be accepted? The probability that the whole batch is accepted a (Round to three decimal places as needed.) Docs the result in (a) suggest that the entire batch consists of good CDs? Why or why not? Yes. because it >> not unlikely that the batch will be accepted. Yes. because if all three CDs in the sample are good then the entire batch must he good. No. because only a probability of 1 would indicate the entire batch consists of good CDs.. No. because the sample will always consist of good CDs.

Explanation / Answer

Let a success be getting a defective one.

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    1463      
K = number of successes in the population =    150      
n = sample size =    3      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.722702136 [ANSWER]

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OPTION C: No, because only a probability of 1 would indicate the entire batch consists of good CDs. [ANSWER]

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