An Engineering Project has the following activities whose time estimates are listed below:

Activity Estimated duration (in months)

Optimistic Most likely Pessimistic 1-2 2 2 14 1-3 2 8 14 1-4 4 4 16 3-5 4 10 28 4-6 4 10 16 5-6 6 12 30

(i) Draw the project network and find the critical path.

(ii) Find the expected duration and variance for each activity. What is the expected project length?

(iii) Calculate the variance and standard deviation of the project length.

(iv) What is the probability that the project will be completed at least eight months earlier than expected time?

(v) If the project due date is 38 months, what is the probability of not meeting the due date?

Given:

Z : 0.50 0.67 1.00 1.33 2.00 Prob.: 0.3085 0.2514 0.1587 0.0918 0.0228