The characteristics of an industrial filling process in which an expensive liqui

Question

The characteristics of an industrial filling process in which an expensive liquid is injected into a container was investigated. The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation 0.02 units. Each unit of fill costs $20 per unit. If a container contains less than 10 units (that is, is underfilled), it must be reprocessed at a cost of $11.

A properly filled container sells for $235.

Complete parts a through c.

a. Find the probability that a container is underfilled.

(Round to four decimal places as needed.)

Find the probability that a container is not underfilled.

(Round to four decimal places as needed.)b. A container is initially underfilled and must be reprocessed. Upon refilling, it contains 10.50 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?

$

Explanation / Answer

a)
P(X < 10)
= P(Z <(10 - 10)/0.02)
=P(Z < 0)
= 0.5
hence probability of underfilled= 0.5
probbaility of not underfilled = 1 - 0.5 = 0.5

b)
profit = 235 - 11 - (20 * 10.5)
= 14

c)
expected profit = 235-11 - (20 * 10.10)
= 22

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