a. Explanation Calculation: The given information is that, the probability that at least one defective item turns up is 0.90, n = 1 , 000 and k = 10 . Assume that lot of n items contains k defectives and n − k items are not defective. The probability of “not defective” is, P ( not defective ) = Number of favorable outcomes Number of possible outcomes = n − k n = n n − k n = 1 − k n Multiplication rule for independent event is P ( A and B ) = P ( A ) × P ( B ) By using the multiplication rule for independent event, the probability of m items are not defective is, P ( m items not defect ) = P ( not defect ) × P ( not defect ) × ... × P ( not defect ) = ( P ( not defect ) ) m = ( 1 − k n ) m The probability of at least one item is defective is, P ( at least one defective item ) = 1 − P ( m item not defective ) = 1 − ( 1 − k n ) m It is given that the probability that at least one defective item turns up is 0.90. Therefore, 1 − ( 1 − k n ) m = 0.90 − 1 + 1 − ( 1 − k n ) m = 0.90 − 1 ( Subtract 1 from both sides ) − ( 1 − k n ) m = − 0 b. To determine Find the value of m when n = 10 , 000 and k = 100 .

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Chapter 1.8, Problem 18P

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Find the value of m when n=1,000 and k=10.

To determine

Find the value of m when n=10,000 and k=100.

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Chapter 1 Solutions

EBK MATHEMATICAL STATISTICS AND DATA AN

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Find the value of m when n = 1 , 000 and k = 10 .

Solution Summary: The author calculates that the probability that at least one defective item turns up is 0.90, n=1,000 and K=10.

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Find the value of m when n=1,000 and k=10.

Find the value of m when n=10,000 and k=100.

Chapter 1 Solutions