LIR 832 FALL 2005 mid-term examination answer key

LIR 832 FALL 2005 mid-term examination answer key - LIR...

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Page 1 of 13 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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Page 2 of 13 B. Calculate the probabilities that 1, 2 3, 4, 5 and 6 toilets are in use mean of x 3 exp(-3) 0.049787068367864 Number of Calls (aka x) mean(x)^x x! P(x) Cumulative Probability 0 1 1 0.04979 0.04979 1 3 1 0.14936 0.19915 2 9 2 0.22404 0.42319 3 27 6 0.22404 0.64723 4 81 24 0.16803 0.81526 5 243 120 0.10082 0.91608 6 729 720 0.05041 0.96649 C. How many toilets do we need to be sure that employees will have to wait for a toilet only 20% of the time? How many do we need to be sure that employees have to wait only 10% of the time. We need to use the cumulative probabilities for this. The likelihood that 4 or fewer toilets will be in use at any time is 86%, so that meets our 81.5% goal (20% of the time they have to wait). The likelihood that 5 or fewer stalls will be in use if 91.6%, so with 6 toilets we should hit our 10% goal.
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Page 3 of 13 2. A global organization with its headquarters in Germany absorbed an American firm several years ago. There is concern among those working for the American subsidiary that they are less likely to be promoted into management (even of the subsidiary) than those working for the parent company.
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This note was uploaded on 07/25/2008 for the course LIR 832 taught by Professor Belman during the Spring '07 term at Michigan State University.

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LIR 832 FALL 2005 mid-term examination answer key - LIR...

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