Consider the office renovation project data in the following table. A "zero" time estimate means that the activity could take a very small amount of time and should be treated as a numeric zero in the analysis.
a. Based on the critical path, find the probability of completing the office renovation project by 38 days. Refer to the standard normal table. (Make sure to round all intermediate calculations for te and variance to two decimal places.)
Time Estimates (days) |
||||
Activity |
Optimistic |
Most Likely |
Pessimisitic |
Immediate Predecessor(s) |
START |
0 |
0 |
0 |
|
A |
5 |
10 |
15 |
START |
B |
0 |
1 |
3 |
A |
C |
15 |
20 |
32 |
A |
D |
3 |
5 |
8 |
B |
E |
2 |
3 |
4 |
D |
F |
8 |
10 |
13 |
C |
G |
0 |
2 |
3 |
D |
H |
1 |
2 |
4 |
G |
I |
2 |
2 |
2 |
C, G |
J |
2 |
3 |
5 |
I |
K |
0 |
1 |
2 |
H |
L |
1 |
2 |
3 |
J, K |
FINISH |
0 |
0 |
0 |
E, F, L |
The critical path is A-C-F
Expected time for the activity A = (5 + 4*10 + 15)/6 = 10
Expected time for the activity C = (15 + 4*20 +32)/6 = 21.16
Expected time for the activity F = (8 + 4*10 + 13)/6 = 10.16
Total estimated time of completion = 10 + 21 + 10 = 41.32 days
Variance for event A = ((15 - 5)/6)2 = 2.7889
Variance for event C = ((8 - 3)/6)2 = 0.6938
Variance for event F = ((13 - 8)/6)2 = 0.6938
Total variance = 2.7889 + 0.6938 + 0.6938 = 4.1765
Standard deviation = 4.1765 =
2.0436
z-score = (38 - 41.32) / 2.0436 = -1.624
Probability (z< -1.624) = 0.0526
Hence, probability of completing the office renovation project by 38 days is 5.26%
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