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. We want to compare the case where these 10 inputs each has a normal distribution with mean 1000 and standard deviation 250 to the case where each has 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 @RISK twice, once with the normally distributed inputs and once 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. Let the output be the minimum of the inputs if this average is less than 1000; otherwise, let the output be the maximum of the inputs.

Skill-Extending Problem