Quick Answer
The answer is 6.67 days. This result comes from the PERT three-point estimate calculation, which uses a weighted average formula: (Optimistic + 4×Most Likely + Pessimistic) / 6. By plugging in the values—4 days optimistic, 6 days most likely, and 12 days pessimistic—you get (4 + 24 + 12) / 6 = 40 / 6, which equals 6.67 days. On the Certified Associate in Project Management CAPM exam, this question tests your ability to apply the PERT technique for activity duration estimation, a key concept in the Schedule Management knowledge area. A common trap is confusing the PERT formula with a simple average; remember that the most likely estimate is weighted four times heavier to reflect realistic uncertainty. For a quick memory tip, think of the mnemonic “O + 4M + P over 6” to keep the order and weighting straight.
This CAPM practice question tests your understanding of project management fundamentals and core concepts. Read the scenario carefully and evaluate each option against the stated constraints before committing to an answer. After answering, compare your reasoning against the explanation and wrong-answer breakdown below. Once you have made your selection, read the full explanation to reinforce the concept and understand why each distractor is designed to mislead on exam day.
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?
Clue words in this question
Noticing these words before you look at the options changes how you read each choice.
Clue: "most likely"
Why it matters: Probability qualifier — the question wants the most probable cause or outcome, not a guaranteed one. Eliminate low-probability options.
6.67 days
Correct PERT calculation: (4 + 4*6 + 12)/6 = 6.67.
12 days
Why wrong: This is the pessimistic estimate.
7.33 days
Why wrong: This would be the simple average.
6 days
Why wrong: This is the most likely estimate.
Answer choices
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.
Key principle: Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option.
Answer analysis
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
Correct PERT calculation: (4 + 4*6 + 12)/6 = 6.67.
Clue confirmation
The clue word "most likely" in the question point toward this answer.
Related concept
Read the scenario before looking for a memorised answer.
12 days
Why it's wrong here
This is the pessimistic estimate.
7.33 days
Why it's wrong here
This would be the simple average.
6 days
Why it's wrong here
This is the most likely estimate.
Common exam traps
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.
Detailed technical explanation
The PERT (Program Evaluation and Review Technique) formula assumes a beta distribution, which is more realistic for project tasks than a normal distribution because it can be skewed. The weights (1,4,1) reflect that the most likely estimate is four times as probable as the extremes, and dividing by 6 normalizes the sum. In real-world scenarios, this method helps project managers account for uncertainty in tasks like software development or construction, where optimistic and pessimistic outcomes are possible.
Key takeaway
Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option.
Real-world example
A practitioner preparing for the CAPM exam encounters this exact type of scenario on the job. The correct answer here is not the most general option — it is the best answer for the specific constraint described. Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option. Real exam questions reward reading the full scenario before eliminating options, because the constraint defines which answer fits.
What to study next
Identify which exam domain this question belongs to, review the core concept, then practise similar questions from the same domain.
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FAQ
Project Management Fundamentals and Core Concepts — This question tests Project Management Fundamentals and Core Concepts — Read the scenario before looking for a memorised answer..
The correct answer is: 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.
Identify which exam domain this question belongs to, review the core concept, then practise similar questions from the same domain.
Yes — watch for: "most likely". Probability qualifier — the question wants the most probable cause or outcome, not a guaranteed one. Eliminate low-probability options.
Read the scenario before looking for a memorised answer.
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Same concept, more angles
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?
mediumWhy D: Option D is correct. PERT expected = (O + 4M + P)/6 = (10 + 4*14 + 20)/6 = (10 + 56 + 20)/6 = 86/6 = 14.33 days.
Last reviewed: Jun 11, 2026
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