A decision maker must choose between two operational plans:
Plan X: Guarantees a performance level that meets 90% of the target.
Plan Y: Offers a 60% chance of exceeding the target by 20% and a 40% chance of falling short by 10%.
Question:
Assuming the decision maker is risk-neutral and based solely on the expected outcome, which plan should be preferred?
Show answer & explanation
Correct answer: B
Explanation
Correct Answer: Plan Y
1. Expected Result of Plan X:
This plan guarantees 90% of the target is achieved.
Expected Result = 90%
2. Expected Result of Plan Y:
Exceeding the target by 20% means: 100% + 20% = 120% (probability = 60% or 0.6)
Failing the target by 10% means: 100% − 10% = 90% (probability = 40% or 0.4)
Now let's calculate its expected value:
Expected Result = (120 × 0.6) + (90 × 0.4)
Expected Result = 72 + 36 = 108%