a$)$ By using PERT, calculate the mean and standard deviation of the project duration. b$)$ By using PERT, calculate the $90$th percentile c$)$ By using PERT, calculate the probability that the project can be completed within $60$ days d$)$ Simulate the completion of this project $100,000$ times assuming that activity times follow triangular distributions. Estimate the mean and standard deviation of the project completion time using simulation output. e$)$ By using the simulation output, estimate the $90$th percentile f$)$ By using the simulation output, estimate the probability that the project can be completed within $60$ days.