A PERT network has nine 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

Question

Question

This question was previously asked in

UPPSC AE Mechanical 2022 Official Paper I (Held on 29 May 2022)

Answer 1

Concept:

In CPM:

The standard deviation of the critical path:

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

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

Where, σ1, σ2, ...., σ8, σ9 are the standard deviation of each activity on the critical path

Calculation:

Given:

σ1, σ2, ...., σ8, σ9 = 3

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

σcp = \(\sqrt {3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2} \)

σcp = \(\sqrt {9 \times 9} \) = 9

∴ the standard deviation of the critical path is 9.