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Making handcrafted pottery generally takes two major

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

Solution for problem 66E 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 66E

Making handcrafted pottery generally takes two major steps: wheel throwing and fi ring. The time of wheel throwing and the time of fi ring are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively.

(a) What is the probability that a piece of pottery will be finished within 95 minutes?

(b) What is the probability that it will take longer than 110 minutes?

Step-by-Step Solution:

Answer

Step 1 of 2</p>

(a)

We are asked to find the probability that a piece of pottery will be finished within

Let  denote the total time.

Let  denote wheel throwing.

Let  denote wheel firing.

Then, ……….(1)

We need to find

If   are independent, normal random variables

Then we can write,

…….(2)

………(3)

Hence the mean and standard deviation of the total time of wheel throwing and the time of firing using equation

……….(4)

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

Since total time follows normal distribution, we can write,

Using  table, the area to the left of  is  

Hence the probability that a piece of pottery will be finished within  is

Step 2 of 2

Chapter 5.4, Problem 66E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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