Question 1051541: The Vending Machine Problem
Have you ever encountered an automatic vending machine with hot drinks at UCLA, another
college campus, or maybe a highway rest area? The intended sequence of events runs something
like this: You insert your money into the machine and select your preferred beverage. A cup falls
out of the machine, landing upright. Liquid streams out of the machine's pour spout until the cup
is nearly full. You reach in, grab the piping hot cup, and drink happily.
Sometimes, things go wrong. The machine might eat your money. Or the cup might not release
until after the liquid has been poured. More frequently, everything goes smoothly until the liquid
begins to flow. It might stop flowing when the cup is only half full. Alternatively, the liquid
might keep on coming until your cup overflows. Neither of these results leaves you satisfied.
The vending machine company wants to keep customers like you happy. So they have decided
to hire your group as statistical consultants. They provide you with the following information:
Cups will hold 8 ounces.
The amount of liquid dispensed varies approximately Normally about the mean weight
programmed into the machine.
standard diviation of 0.2 ounces.
You cannot adjust the variability of the machine without substantial, unacceptable added
costs.
A cup of hot beverage costs the customer $0.50, and the company spends $0.10 for the cup
and $0.02 per ounce.
Perform statistical and cost analyses to determine what mean amount of liquid dispensed should
be programmed into the machine. Support your calculations with clear explanations. The end
product should be a report to the vending machine company CEO
Answer by solver91311(24713)   (Show Source):
|
|
|
