Question

Consider the following PERT network:


The optimistic time, most likely time and pessimistic time of all the activities are given in the table below:

Activity	Optimistic time (days)	Most likely time (days)	Pessimistic time (days)
1 - 2	1	2	3
1 - 3	5	6	7
1 - 4	3	5	7
2 - 5	5	7	9
3 - 5	2	4	6
5 - 6	4	5	6
4 - 7	4	6	8
6 - 7	2	3	4

The standard deviation of the critical path is

• A. 0.33
• B. 1.66
• C. 0.55
• D. 0.88

Answer 1

The correct option is D 0.88

$\sum {\sigma }^2\text{along the critical path}$

$\sum {\sigma }^2={\sigma }_{1-3}^2+{\sigma }_{3-5}^2+{\sigma }_{5-6}^2+{\sigma }_{6-7}^2$

$=\frac{4}{36}+\frac{16}{36}+\frac{4}{36}+\frac{4}{36}=\frac{28}{36}=0.882$

Standard deviation of critical path is

$\sigma =\sqrt{\frac{28}{36}}=0.88$