Correct Answer - Option 2 : 9

__Concept:__

**In CPM:**

The standard deviation of critical path:

σ_{cp }= \(\sqrt {Sum\;of\;variance\;along\;critical\;path} \)

σ_{cp} = \(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

Where, σ_{1}, σ_{2}, ...., σ_{8}, σ_{9} are the standard deviation of each activity on the critical path

__Calculation:__

__Given:__

σ1, σ2, ...., σ8, σ9 = 3

σcp = \(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

σ_{cp} = \(\sqrt {3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2} \)

σ_{cp} = \(\sqrt {9 \times 9} \) = 9

∴ the standard deviation of the critical path is** 9.**