According to the PMBOK® Guide, specifically within the Estimate Activity Durations process, the Three-Point Estimating technique is used to improve the accuracy of activity duration estimates by considering estimation uncertainty and risk.
There are two commonly used formulas for three-point estimating. Unless otherwise specified, the PERT (Program Evaluation and Review Technique) or Beta Distribution is typically used in PMP exams:
Optimistic ($O$): 2 weeks (best-case scenario)
Most Likely ($M$): 5 weeks (realistic scenario)
Pessimistic ($P$): 14 weeks (worst-case scenario)
The Beta Distribution (PERT) Formula:
$$E = \frac{O + 4M + P}{6}$$
Step-by-Step Calculation:
Multiply the Most Likely duration by 4: $4 \times 5 = 20$
Add the Optimistic and Pessimistic durations: $2 + 20 + 14 = 36$
Divide the total by 6: $36 / 6 = 6$
The expected duration ($E$) is 6 weeks.
Note on Triangular Distribution:
If the question had asked for a simple average (Triangular Distribution), the formula would be $(O + M + P) / 3$.
Calculation: $(2 + 5 + 14) / 3 = 21 / 3 = 7$ (Choice D). However, PMP standards favor the weighted Beta/PERT average because it places more weight on the " Most Likely " outcome, making it more statistically accurate for most projects.
Analysis of choices:
Choice A (One): Incorrect calculation.
Choice B (Five): This is just the " Most Likely " value, not the weighted expected duration.
Choice C (Six): Correct based on the PERT formula.
Choice D (Seven): Incorrect as it represents the simple Triangular average rather than the standard PERT estimate.
