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A high-volume printer produces minor print-quality errors

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

Solution for problem 104E 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 104E

A high-volume printer produces minor print-quality errors on a test pattern of 1000 pages of text according to a Poisson distribution with a mean of 0.4 per page.

(a) Why are the numbers of errors on each page independent random variables?

(b) What is the mean number of pages with errors (one or more)?

(c) Approximate the probability that more than 350 pages contain errors (one or more).

Step-by-Step Solution:

Step 1 of 5:

Let X follows the Poisson distribution with the probability density function

  P(X = x) =

Where, = 10,000.

The claim is to find the probability of more than 20,000 hits in a day.

Then, P(X  20000.5) = P(Z )

                                  = P(Z 100.005)

                                  = 0 ( from the area under normal curve table)

Hence, the probability of more than 20,000 hits in a day is 0.

Step 2 of 5:

b) the claim is to find the probability of less than 9900 hits in a day.

   Then, P(X < 9899.5) = P(Z )

                                  = P(Z -1.01)

                                  = 0.1562. ( from the area under normal curve table)

Hence, the probability of less than 9900 hits in a day is 0.1562.

Step 3 of 5:

c)  the claim is to find the probability that the number of hits in a day exceeds the value is 0.01

Then, P(X > x) = 0.01

  =

                     = 2.33

(x + 0.5) - 10000 = 233

x = 10232.5

Hence, x = 10232.5.

Step 4 of 5

Chapter 4.7, Problem 104E is Solved
Step 5 of 5

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, pages, page, mean, pattern. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. The full step-by-step solution to problem: 104E from chapter: 4.7 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. The answer to “A high-volume printer produces minor print-quality errors on a test pattern of 1000 pages of text according to a Poisson distribution with a mean of 0.4 per page.(a) Why are the numbers of errors on each page independent random variables?(b) What is the mean number of pages with errors (one or more)?(c) Approximate the probability that more than 350 pages contain errors (one or more).” is broken down into a number of easy to follow steps, and 65 words. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. Since the solution to 104E from 4.7 chapter was answered, more than 870 students have viewed the full step-by-step answer.

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