A decision maker is working on a problem that requires her to study the uncertainty surrounding the payoff of an investment. There are three possible levels of payoff, i.e., $1,000, $5,000, and $10,000. As a rough approximation, the decision maker believes that each possible payoff is equally likely. But she is not fully comfortable with the assessment that each probability is exactly 1/3, and so would like to conduct a sensitivity analysis. In fact, she believes that each probability could range from 0 to 0.5 following the uniform distribution. The sum of the probabilities must be equal to 1.

(1) Develop an Excel worksheet to capture the above scenario.

(2) Run @Risk to perform the Monte Carlo simulation (using the uniform distribution and 500 iterations) that could facilitate a sensitivity analysis of the probabilities of the payoffs. (3) Attach the simulation graph result for the expected payoff as an output. (4) Based upon the graph result, what is the probability that the payoff will be less than $6,000