Chapter 17 – Project Management
8.
Path
Expected
Duration
Variance
Std. Dev.
A
10
1.21
1.100
B
8
2.00
1.414
C
12
1.00
1.000
D
15
2.89
1.700
E
14
1.44
1.200
Path A:
Probability of completion ≤ 16 weeks = 1.0000 (z value > +3.00—treat probability of completion
as being = 1.0000)
Path B:
Path D:
Using Appendix B Table B: Probability of completion ≤ 16 weeks = 0.7224
Chapter 17 – Project Management
b. Probability (Time ≤ 15 weeks):
Path A:
Probability of completion ≤ 15 weeks = 1.0000 (z value > +3.00—treat probability of completion
as being = 1.0000)
Path B:
Path E:
Using Appendix B Table B: Probability of completion ≤ 15 weeks = 0.7967
Chapter 17 – Project Management
17–23
c. Probability (Time ≤ 13 weeks):
Path A:
as being = 1.0000)
Path C:
Using Appendix B Table B: Probability of completion ≤ 13 weeks = 0.8413
Using Appendix B Table B: Probability of completion ≤ 13 weeks = 0.2033
17–24
Education.
9. Given:
Path
Activity
Mean
Standard
Deviation
A
C
5
1.3
D
4
1.0
B
E
8
1.6
Probability (T > 10 weeks):
Path A:
Expected duration = 5 + 4 = 9
Standard deviation:
Using Appendix B Table B: Probability of completion ≤ 10 weeks = 0.7291
Path B:
Expected duration = 8
Standard deviation = 1.600
Chapter 17 – Project Management
17–25
Education.
10. Given:
The project described below is scheduled to be completed in 11 weeks.
Path
Activity
Mean
Standard
Deviation
A
C
4
0.70
D
6
0.90
B
E
3
0.62
F
9
1.90
a. If you were the manager of this project, would you be concerned? Explain.
Probability (T ≤ 11 weeks):
Variance =
Standard deviation =
Using Appendix B Table B: Probability of completion ≤ 11 weeks = 0.8106
Variance =
Standard deviation =
Using Appendix B Table B: Probability of completion ≤ 11 weeks = 0.3085
Chapter 17 – Project Management
17–26
Education.
b. If there is a penalty of $5,000 a week for each week the project is late, what is the probability
of incurring a penalty of at least $5,000?
This question is asking what the probability will be that the project will take at least 12 weeks
(which would be 1 week late).
Using Appendix B Table B: Probability of completion < 12 weeks = 0.9599
Path B:
Using Appendix B Table B: Probability of completion < 12 weeks = 0.5000
Chapter 17 – Project Management
11. Given:
We are given the following times (optimistic, most likely, and pessimistic) for each activity in the
table below.
a. Determine the expected completion time for each path and its variance.
Activity
Optimistic
Most
Likely
Pessimistic
Mean
Variance
1-2
8
8
8
8.00
0/36
2-3
11
12
13
12.00
4/36
2-4
5
6
7
6.00
4/36
2-5
10
12
14
12.00
16/36
3-8
9
10
12
10.17
9/36
4-6
14
18
26
18.67
144/36
4-7
13
13
13
13.00
0/36
5-9
7
10
12
9.83
25/36
6-11
8
10
14
10.33
36/36
7-11
10.5
13
15.5
13.00
25/36
8-11
5
7
10
7.17
25/36
9-10
10
11
12
11.00
4/36
10-11
6
6
6
6.00
0/36
Path 1-2-3-8-11:
Expected completion time = 8.00 + 12.00 + 10.17 + 7.17 = 37.34
Variance = 0/36 + 4/36 + 9/36 + 25/36 = 38/36
Standard deviation =
Path 1-2-4-6-11:
Expected completion time = 8.00 + 6.00 + 18.67 + 10.33 = 43.00
Variance = 0/36 + 4/36 + 144/36 + 36/36 = 184/36
17–28
Education.
Expected completion time = 8.00 + 12.00 + 9.83 + 11.00 + 6.00 = 46.83
Variance = 0/36 + 16/36 + 25/36 + 4/36 + 0/36 = 45/36
Standard deviation =
b. Determine the probability that the project will require more than 49 weeks.
Probability (T > 49 weeks):
Path 1-2-3-8-11:
Path 1-2-4-7-11:
Probability of completion ≤ 49 weeks = 1.0000 (z value > +3.00—treat probability of
completion as being = 1.0000)
Path 1-2-5-9-10-11:
17–29
Education.
c. Determine the probability that the project will be completed in 46 weeks or less.
Probability (T ≤ 46 weeks):
Path 1-2-3-8-11:
Probability of completion ≤ 46 weeks = 1.0000 (z value > +3.00—treat probability of
completion as being = 1.0000)
Path 1-2-5-9-10-11:
Chapter 17 – Project Management
17–30
Education.
12. Given:
We are given the following times (optimistic, most likely, and pessimistic) for each activity in the
table below.
Activity
Optimistic
Most
Likely
Pessimistic
Mean
Variance
A
2
4
6
4.00
16/36
D
6
8
10
8.00
16/36
E
7
9
12
9.17
25/36
H
2
3
5
3.17
9/36
F
3
4
8
4.50
25/36
G
5
7
9
7.00
16/36
B
2
2
3
2.17
1/36
I
2
3
6
3.33
16/36
J
3
4
5
4.00
4/36
K
4
5
8
5.33
16/36
C
5
8
12
8.17
49/36
M
1
1
1
1.00
0/36
N
6
7
11
7.50
25/36
O
8
9
13
9.50
25/36
End
a. Construct a network diagram.
H
O
1
6
A
B
C
I
J
G
F
Start
2
4
8
1
1
5
D
M
E
N