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# A manufacturer of integrated circuit chips wishes to

ISBN: 9780321629111 32

## Solution for problem 100E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 100E

A manufacturer of integrated circuit chips wishes to control the quality of its product by rejecting any batch in which the proportion of defective chips is too high. To this end, out of each batch (10,000 chips), 25 will be selected and tested. If at least 5 of these 25 are defective, the entire batch will be rejected. a. ?What is the probability that a batch will be rejected if 5% of the chips in the batch are in fact defective? b. ?Answer the question posed in (a) if the percentage of defective chips in the batch is 10%. c. ?Answer the question posed in (a) if the percentage of defective chips in the batch is 20%. d. ?What happens to the probabilities in (a)–(c) if the critical rejection number is increased from 5 to 6?

Step-by-Step Solution:

Answer Step 1 of 5 Given n=25, x=5 The pmf of binomial distribution is P(X)=n cp q n; x=0,1,....,n Step 2 of 5 a)The probability that a batch will be rejected if 5% of the chips in the batch are defective Here p=0.05, q=0.95 P(batch is rejected)=P(x5) =1-P(x<5) =1-P(0)-P(1)-P(2)-P(3)-P(4) =0.0072 Step 3 of 5 b)The probability that a batch will be rejected if 10% of the chips in the batch are defective Here p=0.1, q=0.9 P(batch is rejected)=P(x5) =1-P(x<5) =1-P(0)-P(1)-P(2)-P(3)-P(4) =0.098

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321629111

This full solution covers the following key subjects: batch, chips, defective, Question, rejected. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. Since the solution to 100E from 3 chapter was answered, more than 466 students have viewed the full step-by-step answer. The answer to “A manufacturer of integrated circuit chips wishes to control the quality of its product by rejecting any batch in which the proportion of defective chips is too high. To this end, out of each batch (10,000 chips), 25 will be selected and tested. If at least 5 of these 25 are defective, the entire batch will be rejected. a. ?What is the probability that a batch will be rejected if 5% of the chips in the batch are in fact defective? b. ?Answer the question posed in (a) if the percentage of defective chips in the batch is 10%. c. ?Answer the question posed in (a) if the percentage of defective chips in the batch is 20%. d. ?What happens to the probabilities in (a)–(c) if the critical rejection number is increased from 5 to 6?” is broken down into a number of easy to follow steps, and 136 words. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The full step-by-step solution to problem: 100E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9.

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