Acceptance Sampling

Question

Many manufacturing companies use a quality control procedure called acceptance sampling to make sure that a specific production batch is up to their standards. To do this, a sample of the items from the production batch is randomly selected without replacement and the entire production batch is accepted (and sent out to stores) if every item in the sample is okay.

The ABCD Electronics Company has just manufactured 6500 write-rewrite CDs, and 60 are defective (although they don't know this). Rather than test all the CDs, they use acceptance sampling and randomly select 4 of the CDs for testing. What is the probability that all 4 of the CDs sampled will be okay and the entire batch will be accepted?

Answer 1

This is a hypergeometric distribution problem

out of 6500 CD we are going to select 4, so the sample space is C(6500,4) = 7.430896727 E+13

we want to select 0 out of 60 defectives, so the number of samples of that is C(60,0) = 1

we want to select 4 out of 6440 non-defectives, so the number of samples of that is C(6440,4) = 7.160239221 E+13

number of samples that have okay CDs = 1 * 7.160239221 E+13

probability = 7.160239221 E+13/7.430896727 E+13 = 7.160239221/ 7.430896727 = 0.963576737