An initial investment of \(\$ 22,500\) results in independent annual receipts of \(\$ 6,250\) until the end of the project life. The probability distribution for the project's life is shown in the table below. MARR is 15 percent/year.

For the following questions, determine an analytical solution:

a. Determine the probability that the present worth of the project is greater than 0 .

b. Determine the probability that the present worth of the project is greater than \(\$ 1,000\).
For the following questions, determine a simulation solution using @RISK:

c. Using a Latin hypercube simulation with 10,000 iterations, estimate the mean and standard deviation of present worth and the probability of positive present worth.

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Life (Years) Probability 4 0.10 5 0.25 6 0.45 7 0.15 8 0.05