Question

A project comprises of seven activities. The expected durations of activities and their variances are as follows: \[ \begin{array}{|c|c|c|} \hline \text{Activity} & \text{Expected duration (min)} & \text{Variance (min)} \\ \hline A & 4 & 1 \\ B & 5 & 1 \\ C & 4 & 1 \\ D & 1 & 0 \\ E & 7 & 4 \\ F & 6 & 1 \\ G & 8 & 4 \\ \hline \end{array} \] The critical path consists of activities B, E and G. The standard deviation (in minute) of the project duration is \(\underline{\hspace{2cm}}\). [round off to two decimal places]

Hint:

In PERT analysis, the project variance is the sum of variances along the critical path—only the critical activities contribute to schedule uncertainty.

Answer 1

Correct Answer: 2.9 - 3.1

The project duration variability depends only on the critical path activities: \[ B, E, G \] Their variances are: \[ \sigma_B^2 = 1, \sigma_E^2 = 4, \sigma_G^2 = 4 \] The variance of the total project duration is the sum of variances of critical activities: \[ \sigma_{project}^2 = 1 + 4 + 4 = 9 \] Thus, the standard deviation is: \[ \sigma_{project} = \sqrt{9} = 3.0 \] Hence the answer lies within: \[ \boxed{2.90\text{ to }3.10\ \text{minutes}} \]