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.