The table below presents a project that needs to be scheduled using PERT. Activity Immediate Predecessor(s) Times (Days) a m b A None 1 3 5 B A 1 2 3 C A 1 2 3 D A 2 4 6 E B 3 4 11 F C, D 3 4 5 G E, F 1 4 6 (a) Draw the network. Only nodes and directed arrows are required in the network for full credit. Hint: Add a dummy start node with 0 activity time. (b) Calculate the expected activity time and the variance of activity time for each activity. (c) List all the paths in the network and determine the expected completion time of each path. (d) Which path is the critical path? And why? (e) What is the expected project completion time? (f) What is the variance of the project completion time? Please provide at least one step of calculation and the correct answer for full credit. (g) What is the probability of completing the project within 14 days? Please provide the formula for calculating the z value, the correct z value, at least one step of calculation, and the correct probability for full credit.