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The number of flaws in bolts of cloth in textile

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

Solution for problem 164E Chapter 3.9

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 164E

Problem 164E

The number of flaws in bolts of cloth in textile manufacturing is assumed to be Poisson distributed with a mean of 0.1 flaw per square meter.

(a) What is the probability that there are two flaws in one square meter of cloth?

(b) What is the probability that there is one flaw in 10 square meters of cloth?

(c) What is the probability that there are no flaws in 20 square meters of cloth?

(d) What is the probability that there are at least two flaws in 10 square meters of cloth?

Step-by-Step Solution:

Solution:

Step 1 of 4:

  Given, the Poisson distribution with a mean of 0.1 flaws per square meter.

                        That is,  

                            The pmf of  Poisson distribution is

                     

  a). To find the probability that there are two flaws in one square meter of cloth.    

    Two flaws in one square meter of cloth are

           

                       

        Therefore, the probability that there are two flaws in one square meter of cloth are 0.004524.


 

Step 2 of 4

Chapter 3.9, Problem 164E is Solved
Step 3 of 4

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

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The number of flaws in bolts of cloth in textile