Considering A and B as two activities of a project, what are the standard deviation of Activity A and B ? Activity A: optimistic time (t₀) = 4 days, most likely time (tL) = 7 days, pessimistic time (tP) = 16 days Activity B: optimistic time (t₀) = 4 days, most likely time (tL) = 6 days, pessimistic time (tP) = 22 days
- AStandard deviation of Activity A = 2 and B = 3Correct
- BStandard deviation of Activity A = 6 and B = 9
- CStandard deviation of Activity A = 4 and B = 6
- DStandard deviation of Activity A = 4.5 and B = 3
Solution
Concept
PERT standard deviation
Formula
σ = (tP − t₀) / 6
Step-by-step solution
1. A: σ = (16 − 4)/6 = 2 days. 2. B: σ = (22 − 4)/6 = 3 days.
Explanation
In PERT the standard deviation of an activity is one-sixth of the range between pessimistic and optimistic time.
Why the other options are wrong
The variances would be 4 and 9, which are not the standard deviations. The other pairs do not equal (tP − t₀)/6 = 2 and 3.
Shortcut
σ = (b − a)/6; variance = σ².
Common mistake
Giving the variance (4 and 9) instead of the standard deviation.
Correct answer: A) Standard deviation of Activity A = 2 and B = 3