Estimating probability of project completion using normal distribution

1. PERT analysis indicates that a project has a mean completion time of 40 weeks, with a standard deviation of 2.8 weeks. Probability that the project can be finished in 35 weeks: P(X<35)

2. Probability that the project will take longer than 42 weeks: P(X>42)

3. Probability that the project will take between 39 to 45 weeks to be completed: P(39

4. What the project will be finished after 38 weeks: P(X>38)

5. You must quote a delivery date to your client. If you wish to have a 97% service level (i.e., 97% chance that you will finish the project by that date), how many weeks from the start of the project should you set as that completion date?