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LIR 832:
Mid-term Examination: Fall, 2005
Each Problem is worth 20 points.
Answer five of the six problems.
Problems
should be answered as thoroughly as you are able.
Partial credit on problems is only
possible if I can locate errors in your calculations; neatness and organization of your
answers is essential
Remember, answer only five of the six problems, if you chose
to answer all, I will select the five with the lowest scores.
1.
Employee morale is affected by working conditions and amenities at the
work site.
Although it is possible to over do the amenities, better
conditions – lunchrooms that are clean and have enough space for the
lunch rush,
sufficient numbers of clean bathrooms, good ventilation and
temperature control – can be shown to improve employees views of work
and employee performance.
Although it seems silly, bathrooms play a critical role in employee attitudes
and the efficiency of a workplace.
If there is too little bathroom space
(aka, number of toilets), people spend considerable time waiting for a
toilet.
They are typically not happy about this and work time is lost while
multiple employees wait.
On the other hand, bathrooms are expensive
both in terms of direct cost, floor space and cleaning time (the only thing
worse than waiting for a toilet is waiting for a dirty toilet).
We are planning a new work site with about 100 employees.
The
planners for the site have asked about bathroom size and the number of
toilets.
Our records indicate that, on average
, 3 toilets are in use at any
one time (don’t ask how we know this).
Given the trade off between the number of toilets and the costs of
bathroom facilities, we would like to have enough toilets so that
employees will only have to wait for a stall 10% of the time.
A.
What type of probability distribution should we use to calculate the
probabilities for the number of toilets in use?
Explain why this is the
correct distribution.
Poisson distribution, which gives us the probability of a
number of events occurring in a fixed time period.

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