A manufacturer ships his products in lots of 20. In order to minimize the number

Question

A manufacturer ships his products in lots of 20. In order to minimize the number of defective items that the manufacturer ships to customers, he samples 6 items from each lot and rejects the lot if there is at least one defective item in the lot. If rejected, the manufacturer tests all of the products in the lot.

a.) How many possible samples of size 6 can be selected if the manufacturer uses simple random sampling with replacement?
b.) What is the probability that the lot will not be rejected if the whole lots actually contains 5 defective items?
c.) What is the probability that the lot will not be rejected if the whole lot contains only 1 defective item?

Explanation / Answer

Use combinations since the selection of the objects is without replacement and without regard to order. a) C(20,6) = 38,760 b) C(15,6) / C(20,6) = 5,005 / 38,760 = 0.1291 c) C(19,6) / C(20,6) = 27,132 / 38,760 = 0.7

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