from abve:
as std deviaiton =(b-a)/6
hence
| Activity |
Optimistic |
|
Likely |
Pessimistic |
|
Mean |
Std dev |
| A |
5 |
|
5 |
7 |
|
5.33 |
0.33 |
| B |
1 |
|
2 |
5 |
|
2.33 |
0.67 |
| C |
5 |
|
5 |
5 |
|
5.00 |
0.00 |
| D |
4 |
|
8 |
13 |
|
8.17 |
1.50 |
| E |
1 |
|
10 |
17 |
|
9.67 |
2.67 |
| F |
1 |
|
5 |
7 |
|
4.67 |
1.00 |
| G |
2 |
|
6 |
9 |
|
5.83 |
1.17 |
| H |
4 |
|
4 |
6 |
|
4.33 |
0.33 |
| I |
2 |
|
7 |
10 |
|
6.67 |
1.33 |
| J |
2 |
|
4 |
7 |
|
4.17 |
0.83 |
| K |
6 |
|
10 |
13 |
|
9.83 |
1.17 |
| L |
2 |
|
6 |
6 |
|
5.33 |
0.67 |
| M |
2 |
|
2 |
3 |
|
2.17 |
0.17 |
| N |
7 |
|
7 |
12 |
|
7.83 |
0.83 |
| Activity |
Early Start |
Early Finish |
Late Start |
Late Finish |
Slack |
| A |
0.00 |
5.33 |
0.00 |
5.33 |
0.00 |
| B |
0.00 |
2.33 |
8.00 |
10.33 |
8.00 |
| C |
5.33 |
10.33 |
5.33 |
10.33 |
0.00 |
| D |
5.33 |
13.50 |
7.17 |
15.33 |
1.83 |
| E |
10.33 |
20.00 |
10.33 |
20.00 |
0.00 |
| F |
13.50 |
18.17 |
15.33 |
20.00 |
1.83 |
| G |
13.50 |
19.33 |
18.50 |
24.33 |
5.00 |
| H |
20.00 |
24.33 |
20.00 |
24.33 |
0.00 |
| I |
24.33 |
31.00 |
24.33 |
31.00 |
0.00 |
| J |
31.00 |
35.17 |
33.50 |
37.67 |
2.50 |
| K |
31.00 |
40.83 |
31.00 |
40.83 |
0.00 |
| L |
35.17 |
40.50 |
37.67 |
43.00 |
2.50 |
| M |
40.83 |
43.00 |
40.83 |
43.00 |
0.00 |
| N |
43.00 |
50.83 |
43.00 |
50.83 |
0.00 |
as acticvity on crtical path (with ) slack are =A ,C ,E ,H , I
,K M,N
thereofre project std deviation=sqrt(sum of variance of
activiities on critical path)
=sqrt(11.194) =3.346
hence probability that the critical path will be finished in 55
days or less​ =P(X<55)
=P(Z<(55-50.83)/3.346)=P(Z<1.25)=0.8944
