Problem 1 Consider the following tasks for a project. Task Time (days) Immediate predecessors ABCDE 3 - 2 A 6 A 2 C 3 A F 3 B G 5 C H 1 C I 1.5 J 2 F,H I (a) Draw the project network and determine the critical path(s) using AOA method and determine the critical path. (10 marks) (b) The project manager felt that CPM should not be used for this project. Instead, the best, worst and most likely time was estimated for each activity and PERT was used. The time to complete the project had a mean of 18.5 days and a standard deviation of 2.15 days. (i) Determine the probability that is will take more than 20 days to finish the project. (2 marks) (ii) The project manager wants to tell the client he is 90% sure the project will be completed by time X. What is the value of X? (3 marks)