CAPM Practice Question: Project Management Fundamentals and Core Concepts
A project manager is estimating the duration of an activity. The optimistic estimate is 4 days, the pessimistic is 12 days, and the most likely is 6 days. Using the PERT three-point estimate, what is the expected duration?
⚠ Common exam trap
The trap here is that candidates often mistakenly use a simple average (add all three and divide by 3) instead of the weighted PERT formula, leading them to choose 7.33 days.
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
6.67 days
The PERT three-point estimate formula is (Optimistic + 4×Most Likely + Pessimistic) / 6. Plugging in the values: (4 + 4×6 + 12) / 6 = (4 + 24 + 12) / 6 = 40 / 6 = 6.67 days. This weighted average gives more influence to the most likely estimate, providing a realistic expected duration.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✓
6.67 days
Why this is correct
The PERT weighted average is (optimistic + 4 × most likely + pessimistic) ÷ 6, giving (4 + 24 + 12) ÷ 6 = 40 ÷ 6 ≈ 6.67 days. Weighting the most likely estimate fourfold accounts for expected variability in the activity's duration.
- ✗
12 days
Why it's wrong here
The pessimistic estimate is only one input to the PERT formula, which yields (4 + 24 + 12) ÷ 6 = 6.67 days. Selecting 12 treats the worst case as the expected outcome, discarding both the optimistic and most likely values; pessimistic figures inform risk reserves, not the weighted mean.
- ✗
7.33 days
Why it's wrong here
PERT computes (4 + 4×6 + 12) ÷ 6 = 6.67 days, not 7.33. The figure 7.33 arises from mistakenly applying the simple arithmetic mean (4 + 6 + 12) ÷ 3, which treats all three estimates as equally weighted and omits the fourfold weighting of the most likely value.
- ✗
6 days
Why it's wrong here
The PERT weighted average is (4 + 4×6 + 12) ÷ 6 = 6.67 days, so 6 days merely restates the most likely estimate and ignores the weighting. It is tempting because the most likely value feels representative, but PERT deliberately pulls the result toward the mean using the optimistic and pessimistic figures.
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Same concept, more angles
1 more way this is tested on CAPM
These questions test the same concept from different angles. Work through them to make sure you can recognise it however the exam phrases it.
Variation 1. A project manager is estimating activity durations. The team provides three estimates: optimistic 10 days, pessimistic 20 days, most likely 14 days. Using the PERT beta distribution, what is the expected duration?
medium- A.14 days
- B.14.67 days
- C.15 days
- ✓ D.14.33 days
Why D: The PERT beta (weighted average) formula is (Optimistic + 4 × Most Likely + Pessimistic) / 6. Substituting the values: (10 + 4×14 + 20) / 6 = (10 + 56 + 20) / 6 = 86 / 6 = 14.33 days. This weighted estimate gives more influence to the most likely value while still accounting for the optimistic and pessimistic extremes.
JA
Written by Johnson Ajibi, MSc IT Security
Senior Network & Security Engineer · founder of Courseiva
This CAPM practice question is part of Courseiva's free PMI certification practice question bank. Courseiva provides original exam-style practice questions with explanations, topic-based practice, mock exams, readiness tracking, and study analytics to help learners prepare for the CAPM exam.