Problem #4: Suppose that you are told that the Expected Time for the critical path on a PERT network is 17.52 weeks, and the Critical Path Variance is 4. (20 points). Hint: you will need to adjust the Variance to calculate Z. a) Suppose the project was supposed to be done in 16 weeks. What is the probability that the project will be finished on or before 16 weeks? (Hint: on the test, I may ask you "What is the probability this project will be late?"). b) This is an extension of (a). Suppose that the project analysts have come back with better estimates of how long some activities will take. Your new Expected time is 17.60 weeks, but your Critical Path Standard Deviation is 1.6 now. Redo the calculation you did for (a) with these new numbers and tell me the probability of being late (in other words, more than 16 weeks to finish project). c) Ignore (a) and (b) for this one and use original problem numbers of 17.52 Expected Time and Variance of 4. Suppose instead that the company will pay $100000 fine if the project is not done in 19 weeks. What is the probability that the company will have to pay this fine? (Hint: think about why they would have to pay the fine. On the test, I may ask you about whether the company should get insurance to protect themselves, and how much they would be willing to pay)