Page 1 of 13LIR 832:Mid-term Examination: Fall, 2005Each Problem is worth 20 points. Answer five of the six problems. Problemsshould be answered as thoroughly as you are able. Partial credit on problems is onlypossible if I can locate errors in your calculations; neatness and organization of youranswers is essential Remember, answer only five of the six problems, if you choseto answer all, I will select the five with the lowest scores.1.Employee morale is affected by working conditions and amenities at thework site. Although it is possible to over do the amenities, betterconditions – lunchrooms that are clean and have enough space for thelunch rush, sufficient numbers of clean bathrooms, good ventilation andtemperature control – can be shown to improve employees views of workand employee performance.Although it seems silly, bathrooms play a critical role in employee attitudesand the efficiency of a workplace. If there is too little bathroom space(aka, number of toilets), people spend considerable time waiting for atoilet. They are typically not happy about this and work time is lost whilemultiple employees wait. On the other hand, bathrooms are expensiveboth in terms of direct cost, floor space and cleaning time (the only thingworse than waiting for a toilet is waiting for a dirty toilet).We are planning a new work site with about 100 employees. Theplanners for the site have asked about bathroom size and the number oftoilets. Our records indicate that, on average, 3 toilets are in use at anyone time (don’t ask how we know this).Given the trade off between the number of toilets and the costs ofbathroom facilities, we would like to have enough toilets so thatemployees will only have to wait for a stall 10% of the time.A.What type of probability distribution should we use to calculate theprobabilities for the number of toilets in use? Explain why this is thecorrect distribution.Poisson distribution, which gives us the probability of a number of events occurring in a fixed time period.
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