Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company. Doug listed the following activity information for this project: A. Draw a project network.B. What are the critical activities and what is the expected project completion time?C. If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project? This table outlines a project management scenario, listing various activities with their respective immediate predecessors and time estimates. The time estimates are categorized into three types: Optimistic, Most Probable, and Pessimistic.| Activity | Immediate Predecessor | Optimistic (weeks) | Most Probable (weeks) | Pessimistic (weeks) ||----------|-----------------------|--------------------|----------------------|--------------------|| A | -- | 1.5 | 2.0 | 2.5 || B | A | 2.0 | 2.5 | 6.0 || C | -- | 1.0 | 2.0 | 3.0 || D | C | 1.5 | 2.0 | 2.5 || E | B, D | 0.5 | 1.0 | 1.5 || F | E | 1.0 | 2.0 | 3.0 || G | B, D | 3.0 | 3.5 | 7.0 || H | G | 3.0 | 4.0 | 5.0 || I | F, H | 1.5 | 2.0 | 2.5 |**Explanation:**- **Activity**: Identifies each task in the project.- **Immediate Predecessor**: The tasks that must be completed before starting the current activity.- **Optimistic Time**: The shortest possible time to complete the activity (if everything goes better than expected).- **Most Probable Time**: The most likely time to complete the activity.- **Pessimistic Time**: The longest time to complete the activity, assuming the worst-case scenario.This table is an essential tool for project managers to plan and execute projects efficiently, providing insights into potential timelines and dependencies.

ANSWER : A)Critical Activities as given data Activity Earliest Start Latest Start Earliest Finish Latest Finish Slack Critical Activity A 0 0 2 2 0 Yes B 2 2 5 5 0 Yes C 0 1 2 3 1 D 2 3 4 5 1 E 5 10 6 11 5 F 6 11 8 13 5 G 5 5 9 9 0 Yes H 9 9 13 13 0 Yes I 13 13 15 15 0 Yes Therefore the critical path will be A-B-G-H-I-Finish Expected Completion time= 2 + 3 + 4 + 4 + 2 = 15 weeks C) Variance of the critical path will be sum of variances of all the critical activities, that is σ2 = 0.03 + 0.44 + 0.44 + 0.11 + 0.03 = 1.05 In Probability Distribution Table, we find 0.99 probability occurs at the value of z = +2.33. Z= T-E(T)/ σ = (T-15) / (1.05)1/2 = 2.23 Or T= 15 + 2.23* (1.05)1/2 =17.4 weeks