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 1651 cds, and 539 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? whats the sample size

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19-03-2018
Mathematics

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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 1651 cds, and 539 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? whats the sample size

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mathmate mathmate · Answer 1 · 2018-03-20T12:04:38+01:00

The problem can be solved using hypergeometric distribution, but for relatively simple cases, we can work it out by reasoning.

Given d=539 defectives in a batch n=1651, and the sampling size is 3.
This means that there are 1651-539=1112 good items.

The probability of picking three good items is therefore
P(GGG)=1112/1651 * 1111/1650 * 1110/1649
=4155544/13612495
=0.30527 (to 5 places of decimal)

Answer: the probability of passing the test is 0.30527 (to 5 decimal places)