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Industrial filling process. The characteristics of an

Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich ISBN: 9780321826237 51

Solution for problem 114E Chapter 4

Statistics for Business and Economics | 12th Edition

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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich

Statistics for Business and Economics | 12th Edition

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Problem 114E

Problem 114E

Industrial filling process. The characteristics of an industrial filling process in which an expensive liquid is injected into a container were investigated in the Journal of Quality Technology (July 1999). The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation .2 units. Each unit of fill costs $20 per unit. If a container contains less than 10 units (i.e., is underfilled), it must be reprocessed at a cost of $10. A properly filled container sells for $230.

a. Find the probability that a container is underfilled. Not underfilled.

b. A container is initially underfilled and must be reprocessed. Upon refilling, it contains 10.60 units. How much profit will the company make on this container?

c. The operations manager adjusts the mean of the filling process upward to 10.10 units in order to make the probability of underfilling approximately zero. Under these conditions, what is the expected profit per container?

Step-by-Step Solution:

Step 1 of 3

a) We have to find the probability that the container is underfilled and not under filled

The container is normally distributed with mean 10 and standard deviation 0.2

Hence  adn .

If the container contains less than 10 units it is under filled

Then we have to find P(Under filled) =

Now

             

             

Then

If the container contains more than or equal to 10 units it is not under filled

Then we have to find P(Not under filled)

Now

             

             

Then

Hence P(Under filled) = 0.5 and P(Not under filled) = 0.5

Step 2 of 3

Chapter 4, Problem 114E is Solved
Step 3 of 3

Textbook: Statistics for Business and Economics
Edition: 12
Author: James T. McClave, P. George Benson, Terry T Sincich
ISBN: 9780321826237

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Industrial filling process. The characteristics of an