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Phoenix water is provided to approximately 1.4 million

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

Solution for problem 100E Chapter 4.7

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 100E

Phoenix water is provided to approximately 1.4 million people who are served through more than 362,000 accounts (http:// phoenix.gov/WATER/wtrfacts.html). All accounts are metered and billed monthly. The probability that an account has an error in a month is 0.001, and accounts can be assumed to be independent.

(a) What are the mean and standard deviation of the number of account errors each month?

(b) Approximate the probability of fewer than 350 errors in a month.

(c) Approximate a value so that the probability that the number of errors exceeds this value is 0.05.

(d) Approximate the probability of more than 400 errors per month in the next two months. Assume that results between months are independent.

Step-by-Step Solution:
Step 1 of 3

Solution 100E

Step1 of 5:

Let us consider a random variable X it presents the number of accounts which had an error with parameters n = 362000 and p = 0.001.

Here our goal is:

a). We need to find the mean and standard deviation of the number of account errors each month.

b). We need to find

c). We need to find the value of ‘x’, when

d). We need to find

Step2 of 5:

a).

Let the random variable X follows binomial distribution with parameters ‘n and p.’ and we know that the mean of the binomial distribution is:

                   

   

Standard deviation of binomial distribution is:

               

                                         

           

 

       

Therefore, mean of X is  and standard deviation of X is

Step3 of 5:

b).

Consider,

                     

                 

         

Where, is obtained from standard normal table(area under normal curve).

(In area under normal curve we have to see in row -0.6 under column 0.04)

Hence,

   

   

Therefore,

Step4 of 5:

c).

Let us consider ‘x’ be value, Then consider:

                                                          []

 ...

Step 2 of 3

Chapter 4.7, Problem 100E is Solved
Step 3 of 3

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: errors, month, Probability, accounts, approximate. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. Since the solution to 100E from 4.7 chapter was answered, more than 1283 students have viewed the full step-by-step answer. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. The answer to “Phoenix water is provided to approximately 1.4 million people who are served through more than 362,000 accounts (http:// phoenix.gov/WATER/wtrfacts.html). All accounts are metered and billed monthly. The probability that an account has an error in a month is 0.001, and accounts can be assumed to be independent.(a) What are the mean and standard deviation of the number of account errors each month?(b) Approximate the probability of fewer than 350 errors in a month.(c) Approximate a value so that the probability that the number of errors exceeds this value is 0.05.(d) Approximate the probability of more than 400 errors per month in the next two months. Assume that results between months are independent.” is broken down into a number of easy to follow steps, and 112 words. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. The full step-by-step solution to problem: 100E from chapter: 4.7 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM.

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