Section A: Work Scheduling (Total Marks: 33 marks) Question 2 (15 marks) Consider a small software development project that involves the following activities: Activity Description Immediate predecessors A Produce software specification None Write test plans Software design A D Software code B E Developer test F Software test D and E B The probable completion times in days) have been estimated as follows: Activity Completion Times (days) Optimistic Most Likely Pessimistic A 4 7 10 B 7 23 27 C 11 14 17 D 10 22 28 E 7 23 27 F 22 29 30 Required: (a) Determine the expected value (mean) and the variance of the completion time for each activity. (b) Assuming that the normal distribution applies, determine the probability that the project will take 77 or less days to complete. (c) Assuming that the normal distribution applies, determine the project time for which the probability that we can complete the project is at least 90%