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The manufacturing of semiconductor chips produces 2%

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 98E Chapter 4.7

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 98E

The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Approximate the following probabilities:

(a) More than 25 chips are defective.

(b) Between 20 and 30 chips are defective.

Step-by-Step Solution:

Step 1 of 4:

The percentage of defective chips produced in the manufacturing of semiconductor is 2%

The chips are independent.

 A lot contains 1000 chips.

We have to find the following probabilities.

More than 25 chips are defective.Between 20 and 30 chips are defective.

Step 2 of 4:

The percentage of defective chips produced in the manufacturing of semiconductor is 2%, p=0.02.

Total number of chips, n=1000.

Let X be the number of defective chips in the manufacturing of semiconductor.

From the given information, it is clear that X~B(1000, 0.02)

So the mean of X,

                                     np= (10000.02).

                                         = 20

The variance of X,

                                    np(1-p)= (10000.020.98).

                                                = 19.6

Since np>5 and n(1-p)>5, normal approximation is valid.

If X is a binomial random variable with parameters n and p,

                                                         Z=

Is approximately a standard normal variable.

Step 3 of 4

Chapter 4.7, Problem 98E is Solved
Step 4 of 4

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. This full solution covers the following key subjects: chips, defective, independent, contains, assume. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. Since the solution to 98E from 4.7 chapter was answered, more than 415 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 98E from chapter: 4.7 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. The answer to “The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Approximate the following probabilities:(a) More than 25 chips are defective.(b) Between 20 and 30 chips are defective.” is broken down into a number of easy to follow steps, and 39 words. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712.

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