Question: Which decision is preferred for the objective of minimizing the risk o

Question

Question:

Which decision is preferred for the objective of minimizing the risk or uncertainty? (Problem involves linking a business situation with a statistics problem utilizing mean and standard deviation with probabilities)

Background Info:

The Company is considering a plant expansion enabling the company to begin production of a new computer product. You must determine whether to make the expansion a medium- or large- scale project. The demand for the new product involves an uncertainty, which for planning purposes may be low demand, medium demand, or high demand. The probability estimates for the demands are 0.20, 0.50, and 0.30, respectively.

Given the following data:

Risk Analysis for Medium-Scale Expansion Demand Annual Profit (x)
$1000s Probability P(x) (x - µ) (x - µ)2 (x - µ)2 * P(x) Low 50 20% -83 6944.44 1388.89 Medium 150 50% 17 277.78 138.89 High 200 30% 67 4444.44 1333.33 µ 133 2 = 2861.11 = 53.49 Risk Analysis for Large-Scale Expansion Demand Annual Profit (x)
$1000s Probability P(x) (x - µ) (x - µ)2 (x - µ)2 * P(x) Low 0 20% -133 17777.78 3555.56 Medium 100 50% -33 1111.11 555.56 High 300 30% 167 27777.78 8333.33 µ 133 2 = 12444.44 = 111.55

Explanation / Answer

we find that in medium scale expansion and in large scale expansion: the strategy for medium demand shows the least variance

For medium level expansion it is 138.89

For large scale expansion it is 555.56

Thus this strategy that corresponds to medium demand is less risky because it corresponds to least variance in medium and well as large level expansion

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