Q2, PERT 5 marks) As a new project that you need to manage, you were not able to get exact estimates for the activity durations. Instead, you were able to get three estimates for each activity: optimistic, most probable, and pessimistic as shown in the table below. Activity Duration (days) Expected Predecessors Sigma time (Sigma)^2 Optimistic Most probable Pessimistic A 5 11 14 10.5 1.5 2.25 B 6 6 18 8 2 4 1 10 13 9 2 4 D 4 7 10 A. B 7 1 1 E 11 14 20 B, C 14.5 1.5 2.25 F 7 16 16 D, E 14.5 1.5 2.25 a. For each activity, calculate its expected time and its standard deviation. b. Identify all paths in this project. c. For each path, calculate the path duration and its standard deviation. d. What is the probability that path A, D, F finishes in more than 29.65 days? e. Your manager is asking you for a time estimate for path A, D, F such that you are 95.44% sure that this path would finish in less than this time