For the task network shown in the diagram below, perform the following: Task B 5 days Task C 2 days Task A 2 days Task D 5 days Task F 5 days Task E 6 days Consider that we have the following three time estimates for each of the tasks. Tasks Optimistic time (to) Pessimistic time (tp) Most likely time (tm) 2 Expected duration (te) A B 1 3 1 5 2 5 3 7 3 12 7 8 D 4 E F 5 2 6 5 a. C. Determine the expected duration of each tasks as well as the total estimate for the project. Include both the total estimate for the project as well as the standard deviation for the total path. Show all work. (11 marks) b. If everything went better than expected what would be the earliest possible time for the project to be completed (earliest completion date) along with the standard deviation. Show all paths (5 marks) If everything went worse than expected what would be the latest possible time for the project to be completed (latest completion date) along with the standard deviation. Show all paths (5 marks) d. Using the results from the PERT distribution, we can attempt to standardize the beta distribution against the normal distribution to answer questions about the probability of completing the project within a given time period. In order to compare our estimated times to the normal distribution we can used a Z-score which is only possible if one knows the parameters of the distribution. To calculate the probability of completing the project (or task) within a certain time period, we need to calculate the Z- score as: X-u Z= o Using the values for Te and the standard deviation from your PERT analysis in (a) determine the following (show all work): 1. Probability to complete the project in 18 days. (2 marks) II. Probability to complete project in 12 days (2 marks)