Consider the network described in the table below
Activity Immediate
Predecessor(s) Pessimistic Probable Optimistic
J -- 15 10 8
K -- 9 8 7
L J 10 6 5
M J 3 3 3
N K,M 9 5 1
O K,M 10 7 4
P L,N 10 8 3
a. Calculate the expected duration of each activity.
b. Calculate the expected duration and variance of the critical path.
c. Calculate the probability that the project will be completed in fewer than 30 time units.
(a) See table below. (b) Tasks J-M-N-P are critical. The sum of their expected durations is 26.00; the sum of their variances is 4.50. (c) The standard deviation along the path is = 2.12; the probability that Duration < 30 is the probability that z < (30 - 26.00)/2.12 = 1.89. The associated normal curve area is 0.97062.
Task Early Start Early Finish Late Start Late Finish Slack Mean Variance
J 0 10.5 0 10.5 0 10.5 1.361111
K 0 8 5.5 13.5 5.5 8
L 10.5 17 19.5 26 9 6.5
M 10.5 13.5 10.5 13.5 0 3 0
N 13.5 18.5 13.5 18.5 0 5 1.777778
O 13.5 20.5 19 26 5.5 7
P 18.5 26 18.5 26 0 7.5 1.361111
Project 26 Project 4.5
Std.dev 2.12132
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