Stat question about CDs

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 ABCD Electronics Company has just manufactured 6500 write-rewrite CDs, and 170 are defective. If 5 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol. 

prob = 

Answer 1

1. The population is large and the sample is small, so the binomial approximation would probably be close enough (I will check results using this), but the correct way is to either use combinatorics or Excel's hypergeometric distribution (which addresses sampling from a finite population).

Using combinatorics, note that 170 of 6500 are defective, 6500 - 170 = 6330 are not defective.

Then, the probability of selecting only non-defectives when selecting 5 is

P(6330, 5)/P(6500, 5) = 6330*6329*6328*6329*6326/(6500*6499*6498*9497*6496) =

1.0147 * 10^19/1.1585 * 10^19 = .8759

The check is using the binomial. Let p = 170/6500 = 17/650. P(selecting 0 out of 5) =

(633/650)^5 = .8759, the same result as above.