# Buusiness Statistics

```An entrepreneur wants to determine whether it would be profitable to establish a gardening service in a local suburb. Theentrepreneur believes that there are four possible levels of demand for this gardening service: Very low demand—1% of thehouseholds would use the service. Low demand—5% of the households would use the service. Moderate demand—10% of thehouseholds would use the service. High demand—25% of the households would use the service. Based on past experiences in othersuburbs, the entrepreneur assigns the following probabilities to the various demand levels: P(High demand) = 0.10 P(Moderatedemand) = 0.20 P(Low demand) = 0.50 P(Very low demand) = 0.20

The entrepreneur has calculated the following profits orlosses (\$) of this garden service for each demand level (over a period of one year):
ACTION
DEMAND
Provide GardenService Do Not Provide Garden Service
Very low -50,000 0 Low 60,000 0 Moderate 130,000 0 High 300,000 0
b. Construct an opportunity loss table.
c. Compute the expected monetary value (EMV) for offer- ing thisgarden service.
d. Compute the expected opportunity loss (EOL) for offer- ing this garden service.
e. Explain the meaningof the expected value of perfect information (EVPI) in this problem.
f. Compute the return-to-risk ratio (RTRR) foroffering this garden service.
g. Based on the results of (c), (d), and (f ), should the entre- preneur offer this gardenservice? Why? Before making a final decision, the entrepreneur conducts a survey to determine demand for the gardeningservice. A random sample of 20 households is selected, and 3 indicate that they would use this gardening service.
h. Revisethe prior probabilities in light of this sample infor- mation. (Hint: Use the binomial distribution to determine theprobability of the outcome that occurred, given a par- ticular level of demand.)
i. Use the revised probabilities in (h) torepeat (c) through (g).```