Question

A linear project is split into six identical activities, each having a, m and b durations of 4, 8 and 10 days, which results in the standard deviation of the duration for the complete project being $X_1$ days. As an alternative attempt at project planning, the earlier-split six activities are clubbed as (1st and 2nd), (3rd and 4th) and (5th and 6th), thus needing to consider only three (now-modified) activities; and the standard deviation of the duration for the complete project is now reported as$X_2$ days. $\text{What will be the ratio}\frac{X_2}{X_1}$?

• A. $\frac{5}{6}$
• B. $\frac{2}{3}$
• C. 1
• D. $\frac{7}{6}$

Answer 1

The correct option is C 1

Case I :

Cast II :

After clubbing the activities



Std. deviation of individual activities

$=\frac{10-4}{6}=1$ (before clubbing)

$\therefore$ Std. deviation of whole project in case-I

Std. deviation of individual activities after clubbing

$=\sqrt{1^2+1^2}=\sqrt{2}$

$\therefore$ Std. deviation of whole project in case-II

$\left(X_2\right)=\sqrt{(\sqrt{2}{)}^2+(\sqrt{2}{)}^2+(\sqrt{2}{)}^2}=\sqrt{6}$

$\therefore \frac{X_2}{X_1}=\frac{\sqrt{6}}{\sqrt{6}}=1$