2. (SHOW YOUR COMPLETE WORK) A project network is shown below, with three time estimates (Optimistic Time-Most Likely Time-Pessimistic Time (in days)) for each activity in the network. 2-4-12 5-6-13 3-4-14 A F 0-0-0 4-6-8 0-0-0 Start End 3-5-10 3-5-7 B 3-4-8 E a. Compute the expected time for each activity in the project network. [7 points) b. Identify and list all possible paths in the project network. Compute the expected duration for each path in the project network. [12 points) c. Identify the critical path(s) in the project network. What is the expected project completion time? [4 points] d. Compute the variance of each activity on the critical path(s). [4 points) e. Determine the project variance and project standard deviation. [4 points) Use the PERT analysis results in 2(c) and 2(e) to answer questions (f), (g), (h), and (i) below: f. What is the probability that the project can be completed within 22 days of its start? [4 points] g. What is the probability that the project can be completed within 16 days of its start? [5 points) h. Determine the project deadline that gives this project a 78% chance of on-time completion. [5 points) i. Determine the project deadline that gives this project a 20% chance of on-time completion. [6 points) Use the appropriate label/unit of measurement in your answers. Leave the numbers in decimal and go up to 5 decimal places for higher accuracy