In an acceptance sampling project each item in a lot of size N = 41 is either de

Question

In an acceptance sampling project each item in a lot of size N = 41 is either defective or good. It is known that there are 15 defective items in the lot. A sample of items of size n = 7 is to be selected from the lot without replacement in such a way that every sample of size 7 has the same probability of being selected. a) How many samples of size n = 7 are possible? b) What is the probability that the sample of seven items selected will have exactly two defective items? c) What is the probability that the sample of seven items selected will have no defective items? d) What is the expected number of defective items in the sample of seven items selected? e) What is the standard deviation of the number of defective items in the sample of seven items selected?

Explanation / Answer

a. 41C7=22481940.... b.15C2*26C5/41C7=0.3072199.... c. 26C7/41C7= 0.02925904... d. E(X)=7*15/41= 2.560976..... e, standard deviation=sqrt(7*(15/41)*(26/41))=1.274376..................

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