According to the PMBOK® Guide, when three estimates are provided (Most Likely, Optimistic, and Pessimistic), the expected duration is calculated using Three-Point Estimating. Unless a " Beta " or " PERT " distribution is explicitly mentioned, the standard practice in many exam contexts for a simple " expected duration " is to use the Beta Distribution (PERT) formula, which provides a weighted average.
The formula for the Beta Distribution (PERT) is:
$$E = \frac{O + 4M + P}{6}$$
Where:
O (Optimistic / Best-case) = 2 weeks
M (Most Likely) = 4 weeks
P (Pessimistic / Worst-case) = 12 weeks
Calculation:
Multiply the Most Likely estimate by 4: $4 \times 4 = 16$
Add the Optimistic and Pessimistic estimates: $16 + 2 + 12 = 30$
Divide the total by 6: $30 / 6 = 5$
Therefore, the expected duration is 5 weeks.
Note on Triangular Distribution:
If the question had required the Triangular Distribution ($E = \frac{O + M + P}{3}$), the result would have been $18 / 3 = 6$ weeks. However, the Beta/PERT distribution is the industry standard for increasing the accuracy of duration estimates by weighting the " Most Likely " scenario more heavily, and " 5 weeks " is the statistically preferred answer in PMI-aligned testing for this specific data set.
