According to the PMBOK Guide, specifically within the Estimate Activity Durations process, the Three- Point Estimating technique (based on the Beta/PERT distribution) is used to improve the accuracy of activity duration estimates by considering uncertainty and risk.
* The Components:
* Optimistic ($O$): 2 months.
* Most Likely ($M$): 4 months.
* Pessimistic ($P$): 12 months (converted from 1 year to maintain consistent units).
* The Formula: The standard Beta distribution (or PERT) formula for the expected duration ($E$) is:
$$E = \frac{O + 4M + P}{6}$$
* The Calculation:
$$E = \frac{2 + 4(4) + 12}{6}$$
$$E = \frac{2 + 16 + 12}{6}$$
$$E = \frac{30}{6}$$
$$E = 5 \text{ months}$$
By using this weighted average, the project manager accounts for the fact that the pessimistic estimate (12 months) has a significant impact on the risk profile of the activity, pulling the " Expected " duration higher than the " Most Likely " duration.
Analysis of Other Options:
* A. Two: This is simply the optimistic estimate; it does not account for the other variables or the weighted average.
* B. Four: This is the " Most Likely " estimate. While it is the most frequent occurrence, the three-point technique is designed to look beyond just the most likely scenario to account for risk.
* D. Twelve: This is the pessimistic estimate, representing the worst-case scenario rather than the calculated expected value.