Buusiness Statistics
An entrepreneur wants to determine whether it would be profitable to establish a gardening service in a local suburb. The entrepreneur believes that there are four possible levels of demand for this gardening service: Very low demand—1% of the households would use the service. Low demand—5% of the households would use the service. Moderate demand—10% of the households would use the service.
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High demand—25% of the households would use the service. Based on past experiences in other
suburbs, the entrepreneur assigns the following probabilities to the various demand levels: P(High demand) = 0.10 P(Moderate
demand) = 0.20 P(Low demand) = 0.50 P(Very low demand) = 0.20
The entrepreneur has calculated the following profits or
losses ($) of this garden service for each demand level (over a period of one year):
ACTION
DEMAND
Provide Garden
Service Do Not Provide Garden Service
Very low -50,000 0 Low 60,000 0 Moderate 130,000 0 High 300,000 0
a. Construct a
decision tree.
b. Construct an opportunity loss table.
c. Compute the expected monetary value (EMV) for offer- ing this
garden service.
d. Compute the expected opportunity loss (EOL) for offer- ing this garden service.
e. Explain the meaning
of the expected value of perfect information (EVPI) in this problem.
f. Compute the return-to-risk ratio (RTRR) for
offering this garden service.
g. Based on the results of (c), (d), and (f ), should the entre- preneur offer this garden
service? Why? Before making a final decision, the entrepreneur conducts a survey to determine demand for the gardening
service. A random sample of 20 households is selected, and 3 indicate that they would use this gardening service.
h. Revise
the prior probabilities in light of this sample infor- mation. (Hint: Use the binomial distribution to determine the
probability of the outcome that occurred, given a par- ticular level of demand.)
i. Use the revised probabilities in (h) to
repeat (c) through (g).
