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 ​$30 per unit. If a container contains less than 10 units​ (that is, is​ underfilled), it must be reprocessed at a cost of ​$12. A properly filled container sells for ​$350. 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?

​$______

Answer 1