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 .

Mathematical Statistics and Data Analysis

3rd Edition

ISBN: 9781111793715

Author: John A. Rice

Publisher: Cengage Learning

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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

Mathematical Statistics and Data Analysis

Ch. 1.8 - Prob. 1P Ch. 1.8 - Prob. 2P Ch. 1.8 - Prob. 3P Ch. 1.8 - Prob. 4P Ch. 1.8 - Prob. 5P Ch. 1.8 - Prob. 6P Ch. 1.8 - Prob. 7P Ch. 1.8 - Prob. 8P Ch. 1.8 - Prob. 9P Ch. 1.8 - Prob. 10P

Ch. 1.8 - Prob. 11P Ch. 1.8 - Prob. 12P Ch. 1.8 - Prob. 13P Ch. 1.8 - Prob. 14P Ch. 1.8 - Prob. 15P Ch. 1.8 - Prob. 16P Ch. 1.8 - Prob. 17P Ch. 1.8 - Prob. 18P Ch. 1.8 - Prob. 19P Ch. 1.8 - Prob. 20P Ch. 1.8 - Prob. 21P Ch. 1.8 - Prob. 22P Ch. 1.8 - Prob. 23P Ch. 1.8 - Prob. 24P Ch. 1.8 - Prob. 25P Ch. 1.8 - Prob. 26P Ch. 1.8 - Prob. 27P Ch. 1.8 - Prob. 28P Ch. 1.8 - Prob. 29P Ch. 1.8 - Prob. 30P Ch. 1.8 - Prob. 31P Ch. 1.8 - Prob. 32P Ch. 1.8 - Prob. 33P Ch. 1.8 - Prob. 34P Ch. 1.8 - Prob. 35P Ch. 1.8 - Prob. 36P Ch. 1.8 - Prob. 37P Ch. 1.8 - Prob. 38P Ch. 1.8 - Prob. 39P Ch. 1.8 - Prob. 40P Ch. 1.8 - Prob. 41P Ch. 1.8 - Prob. 42P Ch. 1.8 - Prob. 43P Ch. 1.8 - Prob. 44P Ch. 1.8 - Prob. 45P Ch. 1.8 - Prob. 46P Ch. 1.8 - Prob. 47P Ch. 1.8 - Prob. 48P Ch. 1.8 - Prob. 49P Ch. 1.8 - Prob. 50P Ch. 1.8 - Prob. 51P Ch. 1.8 - Prob. 52P Ch. 1.8 - Prob. 53P Ch. 1.8 - Prob. 54P Ch. 1.8 - Prob. 55P Ch. 1.8 - Prob. 56P Ch. 1.8 - Prob. 57P Ch. 1.8 - Prob. 59P Ch. 1.8 - Prob. 60P Ch. 1.8 - Prob. 61P Ch. 1.8 - Prob. 62P Ch. 1.8 - Prob. 63P Ch. 1.8 - Prob. 64P Ch. 1.8 - Prob. 65P Ch. 1.8 - Prob. 66P Ch. 1.8 - Prob. 67P Ch. 1.8 - Prob. 68P Ch. 1.8 - Prob. 69P Ch. 1.8 - Prob. 70P Ch. 1.8 - Prob. 71P Ch. 1.8 - Prob. 72P Ch. 1.8 - Prob. 73P Ch. 1.8 - Prob. 74P Ch. 1.8 - Prob. 75P Ch. 1.8 - Prob. 77P Ch. 1.8 - Prob. 78P Ch. 1.8 - Prob. 79P Ch. 1.8 - Prob. 80P

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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