Question

Activities A,B,C and D constitute a small project; their interrelationship, expected duration and standard deviation of this expected duration are shown in the figure, respectively.


With a view to improving the speed of implementation, each of B,C and D are split into three equal segments, maintaining appropriate interrelationships between $A$ and each of these nine segments. What will be the standard deviation of the modified project duration after segmentation (to the nearest 1/10 unit)?

• A. 5.2
• B. 4.6
• C. 6.2
• D. 5.6

Answer 1

The correct option is C 6.2

After splitting of activities, new networking diagram will be as shown

$\begin{array}{cc}4.5& =\sqrt{{\sigma }_B^2+{\sigma }_B^2+{\sigma }_B^2}\\ \Rightarrow 4.5& =\sqrt{3{\sigma }_B^2}\\ \Rightarrow {\sigma }_B& =\sqrt{\frac{(4.5{)}^2}{3}}\\ \text{Similarly,}{\sigma }_C& =\frac{3}{\sqrt{3}},{\sigma }_D=\frac{1.5}{\sqrt{3}}\\ & \text{Standard deviation of total project,}\\ \sigma & =\sqrt{3^2+3{\sigma }_B^2+3{\sigma }_C^2+3{\sigma }_D^2}\\ & =\sqrt{3^2+{4.5}^2+3^2+{1.5}^2}\\ & =6.36\end{array}$