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Solved: In the manufacture of electroluminescent lamps,

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

Solution for problem 67E 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 67E

In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X and Y denote the thickness of two different layers of ink. It is known that X is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and Y is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent.

(a) If a particular lamp is made up of these two inks only, what is the probability that the total ink thickness is less than 0.2337 mm?

(b) A lamp with a total ink thickness exceeding 0.2405 mm lacks the uniformity of color that the customer demands. Find the probability that a randomly selected lamp fails to meet customer specifications.

Step-by-Step Solution:

Answer

Step 1 of 2</p>

(a)

We are asked to find the probability that the total ink thickness is less than

Let  denote the total thickness.

Let  denote the thickness of two different layers of ink.

Then, ……….(1)

We need to find

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

Since total thickness follows normal distribution, we can write,

Using  table, the area to the left of  is  

Hence the probability that the total ink thickness is less than  is

Step 2 of 2

Chapter 5.4, Problem 67E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

This full solution covers the following key subjects: ink, thickness, these, LAMP, layers. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Since the solution to 67E from 5.4 chapter was answered, more than 319 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 67E from chapter: 5.4 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. The answer to “In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X and Y denote the thickness of two different layers of ink. It is known that X is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and Y is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent.(a) If a particular lamp is made up of these two inks only, what is the probability that the total ink thickness is less than 0.2337 mm?(b) A lamp with a total ink thickness exceeding 0.2405 mm lacks the uniformity of color that the customer demands. Find the probability that a randomly selected lamp fails to meet customer specifications.” is broken down into a number of easy to follow steps, and 155 words.

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