Question

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defective unit. The ABCD Electronics Company has just manufactured 4500 write-rewrite CDs, and 50 are defective. If 5 of these CDs are randomly selected and tested, what is the probability that the entire batch will be rejected?

Answer 1

the probability of the defective and non-defective CDs in the total batch of CDs as follows:

p=P(DefectiveCDsinthebatch)
= 50/4500

compute the probability of non-defective CDs as follows:

q = 1 - P(DefectiveCDsinthebatch)
= 1 - 50 / 4500
= 4450/4500

calculate the probability that from the selected sample of 5 CDs, there is no defective CD as follows:

P( X = x) =

  Using Binomial Distribution: P(X = 0) = 0.9461

probability that the entire batch will be rejected is 0.9461