Question

suppose a retailer has two markets, 1 and 2. demand 1 follows normal distribution with mean 100 and standard deviation 12.4. demand 2 follows normal distribution with mean 110 and standard deviation 16.7. the retailer needs to know the mean and standard deviation of the difference between the two demands. please describe the conceptual analysis process to find out these two parameters by using simulation

Answer 1

For market 1, mean (μ₁) = 100, stdev (σ₁) = 12.4
For market 2, mean (μ₂) = 110, stdev (σ₂) = 16.7

For the difference, mean (μ) = μ₂ + (- μ₁)= 110 - 100 = 10
For the difference, variance (σ²) = σ₂² + (- σ₁)² = (16.7)² + (-12.4)² = 432.65; so, stdev (σ) = √432.65 = 20.8

Therefore, Difference ~ Normal (10, 20.8)

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Simulation model

Result

Average	9.9
Stdev	20.6

So, based on simulation: Difference ~ Normal (9.9, 20.6)