The estimated times and immediate predecessors for the activities in a project at George Kyparis's retinal scanning company are given in the following table. Assume that the activity times are independent.
|
Activity
|
Immediate Predecessors
|
Time (Weeks)
|
|
a
|
m
|
b
|
|
A
|
-
|
9
|
10
|
11
|
|
B
|
-
|
4
|
10
|
16
|
|
C
|
A
|
9
|
10
|
11
|
|
D
|
B
|
5
|
8
|
11
|
a) Calculate the expected time and variance for each activity.
b) What is the expected completion time of the critical path? What is the expected completion time of the other path in the network?
c) What is the variance of the critical path? What is the variance of the other path in the network?
d) If the time to complete path A-C is normally distributed, what is the probability that this path will be finished in 22 weeks or less?
e) If the time to complete path B-D is normally distributed, what is the probability that this path will be finished in 22 weeks or less?
f ) Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks or less?