2. A project has been subdivided into five activities. Their immediate predecessors and the estimated activity durations (optimistic, most likely, and pessimistic) are shown in Table 1

Table 1 Details of the network

Activity Immediate Predecessor Estimate duration (in days)

A - 1, 2, 3

B - 1, 3, 5

C A, B 3, 4, 5

D A, C 2, 2, 2

E C, D 1, 2, 21

(a) Draw the project network. Based on the mean activity durations, calculate all earliest and latest starting and finishing times, and the total floats of all activities. What is the critical path? What is its duration?

(b) Calculate the variance and standard deviation on the critical path.

(c) Calculate the probability that the project will be finished between 11 and 15 days.

(d) What is the probability that the project will be finished within 14 days? What is the probability that the project will be finished in exactly 14 days?