The following represents a project that should be scheduled using PERT. Activity Immediate Predecessor(s) Times (Days) a m b A None 1 3 5 B None 1 2 3 C A 1 2 3 D A 2 3 4 E B 3 4 11 F C, D 3 4 5 G D, E 1 4 6 H F, G 2 4 5 (a) Draw the network. Only nodes and directed arrows are required in the network for full credit. Hint: Add a dummy starting node with 0 activity time. (b) What is the critical path? Please calculate the expected activity time for each activity and list the correct critical path for full credit. (c) What is the expected project completion time? Please provide at least one step of calculation and the correct answer for full credit. (d) What is the variance of the project completion time? Please provide at least one step of calculation and the correct answer for full credit. (e) What is the probability of completing this project within 16 days? Please provide the formula for calculating the z value, at least one step of calculation, and the correct probability for full credit.