Question

Consider a PERT network for a project involving six tasks (a to f)

Task	Predecessor	Expected task time (in days)	Variance of the task time (in days${}^2$)
a	-	30	25
b	a	40	64
c	a	60	81
d	b	25	9
e	b, c	45	36
f	d, e	20	9

The standard deviation of the critical path of the project is

• A. $\sqrt{155}days$
• B. $\sqrt{151}days$
• C. $\sqrt{200}days$
• D. $\sqrt{238}days$

Answer 1

The correct option is B $\sqrt{151}days$

For critical path a-c-e-f, the variance for each task is shown below

Task	Variance $\left({\sigma }^2\right)$
a	25
c	81
e	36
f	09

$\text{Total variance = 25 + 81 + 36 + 9 = 151}$

We know that

Standard deviation,

$\sigma =\sqrt{\text{Variance}}$

$\therefore$ S.D. of critical path,

${\sigma }_{cp}=\sqrt{151}days$