The data for a PERT network is given in the following table:

(i) Draw a network and estimate the earliest and latest event times for all nodes and hence derive critical path.
(ii) Estimate the expected duration of the project and corresponding variance.
(iii) What is the probability that the project duration will exceed 60 days?
(iv) What is the chance of completing the project between 45 and 54 days?
(v) What is the probability of completing the project within 30 days? (MBA, Ruhailkhand, 2003)

Activity-nodes (i-j) 1-2 0 Time duration (days) m P 1-3 26 4 6 6 6 1-4 6 12 24 2-3 2 5 8 2-5 11 14 28 3-4 15 24 45 3-6 3 6 9 4-6 9 15 27 5-6 4 10 16 Note: o-optimistic; m-most likely: p-pessimistic