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Simulation can be used to illustrate a number of results from statistics that are difficult to understand with nonsimulation arguments. One is the famouscentral limit theorem, which says that if you sample enough values fromanypopulation distribution and then average these values, the resulting average will be approximately normally distributed. Confirm this by using @RISK with the following population distributions (run a separate simulation for each): (a) discrete with possible values 1 and 2 and probabilities 0.2 and 0.8; (b) exponential with mean 1 (use the RISKEXPON function with the single argument 1); (c) triangular with minimum, most likely, and maximum values equal to 1, 9, and 10. (Note that each of these distributions is very skewed.)

Run each simulation with 10 values in each average, and run 1000 iterations to simulate 1000 averages. What are the means of these averages? If needed, round your answers to three decimal digits.

Of first 10AveragesDiscreteExponentialTriangular

Run each simulation with 30 values in each average, and run 1000 iterations to simulate 1000 averages.

Of all 30AveragesDiscreteExponentialTrianagular