39.

(a) PERT calculations yield the critical path length of a project to be 24 months with a variance of 9. What is the probability of its completion in 20 months? Within how many months would you expect the project to be completed with probability of 0.90?

(b) In a PERT network, the expected duration of the critical path is 36 weeks and the sum of the variances of the activities on the critical path is 36 weeks2• Calculate the probability that the project may be completed not earlier than 30 weeks and not later than 42 weeks.

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c) If, in a PERT network, the expected duration of the critical path is 42 months and the sum of the variances of the activities on the critical path is 36 months2, then the probability that the project may be completed not earlier than 36 months and not later than 48 months is approximately

(i) 50 per cent (ii) 68 per cent (iii) 95 per cent (iv) none of these

(d) The earliest time of completion of a project is the (i) time on the shortest path between start and end events of the project (ii) time on the longest path between start and end events of the project (iii) time on the longest path between any two events of the project (iv) none of the above

(e) An activity in a PERT project has expected duration of 19/3 days, with a standard deviation of I day. Obtain the optimistic and pessimistic durations of it, given that the activity has most likely duration of 6 days.

(f) One of the activities in a PERT project has an estimated duration of 17 weeks and a variance of 16 weeks2• The most likely duration of this activity is shown to be 16 weeks. It can then be inferred that the estimates of the optimistic and pessimistic durations would respectively be:
(i) 12 and 20 weeks (ii) 7 and 31 weeks (iii) 5 and 28 weeks (iv) Not determinable from the given data