What is the formula for calculating activity duration using the beta distribution?

The formula for calculating activity duration using the beta distribution is derived from the concept of expected duration in project management, which incorporates uncertainty in estimating activity durations. The correct calculation combines optimistic, most likely, and pessimistic estimates of the duration.

The correct formula, which indeed is represented by combining these three estimates with a specific weight for the most likely estimate, is calculated as follows:

Take the optimistic estimate (O) and the pessimistic estimate (P), and weight the most likely estimate (M) four times more than the optimistic and pessimistic estimates. Therefore, the formula integrates these elements:

Activity Duration = (O + 4M + P) / 6.

This approach provides a more balanced and statistically sound method of estimating project durations under uncertainty, accounting for the probability distribution of the possible durations where the most likely duration is given more significance. By doing so, it not only improves the accuracy of the estimates but also allows for better project planning and management.

The other options do not adequately represent the beta distribution's approach to estimating activity duration. For instance, a simple average of the three estimates does not weigh the most likely estimate appropriately, and options that only consider two estimates or a ratio of differences fail to encompass the broader range of expected