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A plastic casing for a magnetic disk is composed of two

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

Solution for problem 65E Chapter 5.4

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 65E

A plastic casing for a magnetic disk is composed of two halves. The thickness of each half is normally distributed with a mean of 2 millimeters, and a standard deviation of 0.1 millimeter and the halves are independent.

(a) Determine the mean and standard deviation of the total thickness of the two halves.

(b) What is the probability that the total thickness exceeds 4.3 millimeters?

Step-by-Step Solution:

Answer

Step 1 of 2</p>

(a)

We have given a plastic casing for a magnetic disk is composed of two halves.

The thickness of each half is normally distributed with a mean of  and a standard deviation of  and the halves are independent.

We are asked to find the mean and standard deviation of the total thickness of the two halves.

Let  denote the total thickness.

Then, ……….(1)

If  are independent, normal random variables with

Is a normal random variable with

…….(2)

………(3)

Hence the mean and standard deviation of the total thickness of the two halves using equation

……….(4)

Compare equation (1) and (4), we get

Hence the mean and standard deviation of the total thickness of the two halves is  respectively.

Step 2 of 2

Chapter 5.4, Problem 65E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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