A project was planned using PERT with three time estimates. The expected completion time of the project was determined to be 40 weeks. The variance of the critical path is 9.

a) What is the probability that the project will be finished in 40 weeks or less?

b) What is the probability that the project takes longer than 40 weeks?

c) What is the probability that the project will be finished in 46 weeks or less?

d) What is the probability that the project takes longer than 46 weeks?

e) The project manager wishes to set the due date for the completion of the project so that there is a 90% chance of finishing on schedule. Thus, there would only be a 10% chance the project would take longer than this due date. What should this due date be?