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 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