What is required for calculating the probability that the critical path will be completed by time T?

To calculate the probability that the critical path will be completed by a certain time T in a project, it is essential to have knowledge of the standard deviation for all activities on the critical path. This is because the completion time of the critical path is subject to variability and uncertainty, which can be quantified using the standard deviation.

In project management, especially when applying the Program Evaluation and Review Technique (PERT), the critical path's duration can be modeled as a normal distribution, where the mean is based on the expected durations of activities along that path. The standard deviation reflects the uncertainty and variability associated with the duration of those activities. By understanding the standard deviation, one can compute the probability that the project's critical path will finish by the given time T using statistical methods.

Other factors, such as the total budget or resource availability, do not directly influence the calculation of probability related to the timing of the critical path itself, as they pertain to cost management and resource allocation rather than to the timing and uncertainties of task durations.