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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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The number of flaws in bolts of cloth in textile

Chapter 3, Problem 164E

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QUESTION:

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

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

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

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

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

Questions & Answers

QUESTION:

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

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

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

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

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

ANSWER:

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.

 

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