Problem 3 (15 points) The table below gives different estimates of durations of all tasks in a project.

task A B D E F G H I J K L a (shortest) m (most likely) b (longest) predecessor 8 10 12 none 6 7 9 none 3 3 4 none 10 20 30 A 6 7 8 9 10 11 B,D,E 6 7 10 B,D,E 14 15 16 F 10 11 13 F 6 8 11 G H 4 7 8 1 2 4 G,H I,J 1. (5 points) Estimate the mean and variance of each task. 2. (5 points) Use the mean duration to identify critical path(s), and estimate mean and variance of the project's completion time. 3. (5 points) Use the normal distribution assumption to determine the prob- ability that it will take 65 or more days to complete the project