According to the PMBOK® Guide, specifically within the Estimate Costs process, Three-point estimating is used to define an approximate range for an activity ' s cost, thereby improving the accuracy of the estimate by factoring in uncertainty and risk.

The formula provided in option C is the Beta Distribution, which is historically derived from the Program Evaluation and Review Technique (PERT). This is the most commonly used formula in PMI-based exams when " Three-point estimating " is mentioned without specifying a simple average.

The variables are defined as:

$C_e$ (Expected Cost): The calculated " weighted " average.

$C_o$ (Optimistic Cost): The cost based on a best-case scenario.

$C_m$ (Most Likely Cost): The cost based on a realistic appraisal of the work and expenses.

$C_p$ (Pessimistic Cost): The cost based on a worst-case scenario.

In the Beta Distribution, the Most Likely ($C_m$) estimate is given a weight of 4, while the Optimistic and Pessimistic estimates are given a weight of 1 each. The total weight is 6 ($1 + 4 + 1$), which is why the sum is divided by 6. This " weights " the result toward the most realistic outcome while still allowing the risks (pessimistic) and opportunities (optimistic) to influence the final number.

A, B, and D: These represent mathematically incorrect weightings that do not align with the standard Beta (PERT) or Triangular distribution formulas recognized by PMI.

Triangular Distribution (Alternative): While not listed as an option here, the other common three-point formula is the simple average: $C_e = (C_o + C_m + C_p) / 3$. This is used when there is less historical data available.

This formula is identical to the one used for Three-point Duration Estimating, simply swapping " Time " ($t$) for " Cost " ($c$). It is a primary tool for reducing the bias that often occurs with single-point estimates.