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## Statistics

Problem

Lake Placid Town Council has decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the suitable size. Many influential citizens desire a large center which will be a showcase for the area, but mayor feels that if demand does not support such a center, the community would lose a large amount of money. To give structure for the decision process, council narrowed building alternatives to three sizes: small, medium, and large. Everybody agreed that critical factor in selecting the best size is the number of people who would want to use new facility. A regional planning consultant provided demand estimates under three scenarios: worst case, base case, and best case. Worst-case scenario corresponds to a situation in which tourism drops significantly; the base-case scenario corresponds to a situation in which Lake Placid continues to attract visitors at present levels; and the best-case scenario corresponds to a significant increase in tourism.

The consultant has provided probability assessments of .10, .60, and .30 for the worst-case, base-case, and best-case scenarios, respectively.

The town council suggested using net cash flow over the five-year planning horizon as a criterion for deciding on the best size. A consultant developed following projections of net cash flow (in thousands of dollars) for a five-year planning horizon. All costs, including consultant’s fee, are included.

Demand Scenario
Worst         Base         Best
Center Size            Case         Case         Case
Small                      400         500         660
Medium                 -250         650         800
Large                    -400         580         990

a. What decision must Lake Placid make using the expected value approach?

b. find out the expected value of perfect information. Do you think it will be worth trying to get extra information concerning which scenario is likely to occur?

c. Assume probability of the worst-case scenario increases to .2, the probability of the base-case scenario decreases to .5, and the probability of the best-case scenario remains at .3. What effect, if any, would these changes have on the decision recommendation?

d. The consultant suggested that an expenditure of \$150,000 on a promotional campaign over the planning horizon will effectively reduce the probability of the worst-case scenario to zero. If the campaign can be expected to also increase the probability of the best-case scenario to .4, is it a good investment?

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M92079

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