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 $14. A properly filled containe sells for $235. Complete parts a through c. Complete parts a hrl Click here to view a table of areas under the standardized normal curve 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 reflling, 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) Mean = 10 units

50% of the values lies below mean

So, P(a container is underfilled) = 0.5

P(a container is not underfilled) = 1 - 0.5 = 0.5

B) profit on a refilled container = $235 - $20 - $14

= $201

C) Under new conditions, probability that a container is underfilled = P(X < 10)

= P(Z < (10 - 10.1)/0.02)

= P(Z < - 5)

= 0

So, expected profit = 235 - 20 = $215

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