A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is

The correct option is 9.

To find the standard deviation of the critical path in a PERT (Program Evaluation and Review Technique) network, we use the statistical properties of independent activities along that path.

First, we relate the variance of the critical path to the variances of the individual activities. For a series of independent activities on the critical path, the total variance of the critical path (${\sigma }_p^2$) is the sum of the variances of each individual activity (${\sigma }_i^2$) on that path:
${\sigma }_p^2=\sum _{i=1}^n{\sigma }_i^2$

Here, we are given:
- The number of activities on the critical path, $n=9$
- The standard deviation of each individual activity, ${\sigma }_i$ for all $i$

First, we calculate the variance of a single activity:
${\sigma }_i^2=3^2=9$

Next, we sum the variances of all 9 activities to find the total variance of the critical path:
${\sigma }_p^2=9\times 9=81$

Finally, the standard deviation of the critical path (${\sigma }_p$) is the square root of its total variance:
${\sigma }_p=\sqrt{{\sigma }_p^2}=\sqrt{81}=9$

Therefore, the standard deviation of the critical path is 9.