$.(15$ points$)$ Please determine the time buffer for $95\%$ confidence level using Unified Scheduling Method $($USM$).$

II$.(5$ points$)$ What is the recommended duration of the project based on the above information?

III. $(25$ points$)$ For comparison, now determine the project duration with $95\%$ confidence level using Monte Carlo Simulation in @Risk using only the data for critical path and Discrete Distribution representation of the data provided above. Please include the project duration distribution graph in the PDF file.

IV$.(20$ points$)$ For another comparison, now determine the project duration with $95\%$ confidence level using PERT analysis using only the critical path data.

For PERT analysis, the following formulas can be used for mean and standard deviations of the activities. Again, the formulas provided below can be used for any discrete distributions.