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. The ABC Electronics Company has just manufactured 1500 write-rewrite CDs, and 160 are defective. If 6 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Answer 1

To find the probability that the entire batch will be accepted, we need to find the probability that all 6 CDs selected for testing are not defective. This is known as the probability of a "success" in the binomial distribution, which is (1 - population proportion of defective CDs) raised to the power of the number of CDs selected for testing.

The population proportion of defective CDs is 160/1500 = 0.107. So the probability of a CD being not defective is 1- 0.107 = 0.893. Therefore, the probability of all 6 CDs selected for testing are not defective is (0.893)^6 = 0.827 which is about 83%

Therefore, the probability that the entire batch of 1500 CDs will be accepted if 6 CDs are randomly selected for testing is 0.827 or about 83%.

It's worth noting that this method is based on some assumptions and the actual probability might be different.