please answer using pencil and paper. anything else is unwanted

2. (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. 4-5-12 4-7-13 5-6-10 0-0-0 2-6-7 5-8-14 0-0-0 Start End 3-5-7 1-4-10 4-6-11 H a. Compute the expected time for each activity in the project network. [8 points) b. Identify and list all possible paths in the project network. Compute the expected duration for each path in the project network. [16 points) c. Identify the critical path() in the project network. What is the expected project completion time? 14 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 (1), (g), (h), and () below: f. What is the probability that the project can be completed within 25 weeks of its start? [4 points) g. What is the probability that the project can be completed within 18 weeks of its start? 15 points) h. Determine the project deadline that gives this project an 85% chance of on-time completion. [5 points) i. Determine the project deadline that gives this project a 27% chance of on-time completion. [6 points) Use the appropriate label/unit of measurement in your answers. Go up to 5 decimal places for higher accuracy