The effect of the shapes of input distributions on the distribution of an output can depend on the output function. For this problem, assume there are 10 input variables. The goal is to compare the case where these 10 inputs each have a normal distribution with mean 1000 and standard deviation 250 to the case where they each have a triangular distribution with parameters 600, 700, and 1700. (You can check with

@RISK’s Define Distributions window that even though this triangular distribution is very skewed, it has the same mean and approximately the same standard deviation as the normal distribution.) For each of the following outputs, run two @RISK simulations, one with the normally distributed inputs and one with the triangularly distributed inputs, and comment on the differences between the resulting output distributions. For each simulation run 10,000 iterations.

a. Let the output be the average of the inputs.

b. Let the output be the maximum of the inputs.

c. Calculate the average of the inputs. Then the output is the minimum of the inputs if this average is less than 1000; otherwise, the output is the maximum of the inputs.

Skill-Extending Problems