Final Answer:
To estimate the standard deviation of the critical path's expected time in project management, sum the variances of individual tasks on the critical path. If task standard deviations (σ) are given, square them to obtain variances. The final standard deviation is the square root of the sum of these variances.
Step-by-step explanation:
In project management, the critical path represents the sequence of tasks that determine the overall project duration. To estimate the standard deviation of the critical path's expected time, one employs the Critical Path Method (CPM). Each task on the critical path has an associated variance, which may be derived from historical data or expert judgment. If the standard deviation (σ) for each task is known, the variance (σ^2) is calculated by squaring it.
The standard deviation of the critical path is then determined by summing the variances of individual tasks and taking the square root of this sum.This approach assumes that the tasks on the critical path are independent of each other. If dependencies or correlations exist, a more sophisticated method may be necessary.
Essentially, the formula encapsulates the idea that the variability of individual task durations contributes to the overall uncertainty in the critical path duration. By aggregating these uncertainties, the standard deviation of the critical path provides a measure of the project's overall schedule risk, helping project managers assess the potential variability in project completion times.