1. (SHOW YOUR COMPLETE WORK) A project network is shown below, with three time estimates (Optimistic Time-Most Likely Time-Pessimistic Time (in weeks)) for each activity in the network. 11-18-22 6-11-13 8-12-16 0-0-0 7-13-16 0-0-0 Start End 14-16-21 7-10-13 12-15-21 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. (6 points] c. Identify the critical path(s) in the project network. What is the expected project completion time? [3 points] d. Compute the variance of each activity on the critical path(s). (3 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 49 weeks of its start? [3 points] . What is the probability that the project can be completed within 39.5 weeks of its start? [4 points] h. Determine the project deadline that gives this project a 68% chance of on-time completion. [5 points] i. Determine the project deadline that gives this project a 10% 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