Question

The characteristic of an industrial filling process in which an expensive liquid is injected into a container were investigated in a journal. the injected quantity per container is approximately normally distributed with mean 10 units and SD 2 units. Each hit of fill costs $20 per unit. If a container contains less than 10 units, it must be reprocessed at a cost of $10. A properly filled container sells for $230.

A. Find the probability that a container is under filled. Not undefiled.

B a container is initially undefiled 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 its in order to make the probablity of underselling almost zero. under these conditions what is the expected profit per container?

Answer 1

Sol:

let X~N(10,2²)

mean (mu)= 10

sigma= 2

a).

prob(x<10)

=prob(z<(10-mu)/sigma)

=prob(z<(10-10)/2)

=prob(z<0)

=0.5

b).

Cost of filling 10.60 unit is

= $20×10.60+$10=$(212+10)=$222

And selling price=$240

Profit=$(240-222)=$18

c).

Cost of filling10.10 unit is

=$20×10.10

=202

Selling price= 240

Expected profit=240-202=38

Thus expected profit per container is $38 .

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