Quick Answer
The answer is approximately 97.5%. This probability is derived from the normal distribution, where the critical path duration of 120 days serves as the mean, and the standard deviation is 5 days. Completing the project within 130 days represents a value exactly two standard deviations above the mean, since 130 minus 120 equals 10, and 10 divided by 5 equals 2. In a standard normal curve, roughly 95% of data falls within plus or minus two standard deviations, so the area to the left of the mean is 50%, and half of the 95% (which is 47.5%) lies between the mean and +2σ, giving a total of 97.5%. On the Project Management Professional PMP exam, this concept tests your ability to apply the PERT and standard deviation to calculate schedule probabilities, often appearing in earned value or risk analysis questions. A common trap is forgetting that the 95% rule covers both tails, so you must add only the upper half to the 50% baseline. Memory tip: “Two sigma up, 97.5%—just add half the bell curve’s cup.”
This PMP practice question tests your understanding of process — managing technical aspects. 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 has a critical path of 120 days with a standard deviation of 5 days. The project sponsor wants to know the probability of completing the project within 130 days. Using the normal distribution, what is the approximate probability?
97.5%
97.5% is the probability of completing at or below 2 standard deviations above the mean.
95%
Why wrong: 95% is the probability within 2 standard deviations of the mean (both sides).
84%
Why wrong: 84% corresponds to 1 standard deviation above the mean.
68%
Why wrong: 68% is the probability within 1 standard deviation of the mean.
Answer choices
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
97.5%
The critical path duration is 120 days with a standard deviation of 5 days. Completing within 130 days is 2 standard deviations above the mean (130 - 120 = 10, 10/5 = 2). In a normal distribution, approximately 95% of data falls within ±2 standard deviations, so the probability of being at or below +2σ is 50% + (95%/2) = 97.5%.
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.
97.5%
Why this is correct
97.5% is the probability of completing at or below 2 standard deviations above the mean.
Related concept
Read the scenario before looking for a memorised answer.
95%
Why it's wrong here
95% is the probability within 2 standard deviations of the mean (both sides).
84%
Why it's wrong here
84% corresponds to 1 standard deviation above the mean.
68%
Why it's wrong here
68% is the probability within 1 standard deviation of the mean.
Common exam traps
The trap here is confusing the probability of completing within a range (e.g., ±2σ = 95%) with the cumulative probability up to a single upper limit (+2σ = 97.5%), leading candidates to incorrectly select 95% instead of 97.5%.
Detailed technical explanation
In project scheduling, the normal distribution assumption for critical path duration relies on the Central Limit Theorem, where the sum of independent activity durations approximates normality even if individual activities are not normally distributed. The standard deviation of the critical path is the square root of the sum of variances of activities on the critical path. For a 2-sigma upper tail, the exact probability from the Z-table is 97.72%, but 97.5% is the commonly used approximation for PMP exam purposes.
Key takeaway
Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option.
Real-world example
A small business has 20 workstations on the 192.168.1.0/24 network and one public IP from its ISP. The router uses PAT (NAT overload) so all 20 devices share one public address using different source ports. NAT questions test whether you understand the four address terms and which direction each translation applies.
What to study next
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FAQ
Process — Managing Technical Aspects — This question tests Process — Managing Technical Aspects — Read the scenario before looking for a memorised answer..
The correct answer is: 97.5% — The critical path duration is 120 days with a standard deviation of 5 days. Completing within 130 days is 2 standard deviations above the mean (130 - 120 = 10, 10/5 = 2). In a normal distribution, approximately 95% of data falls within ±2 standard deviations, so the probability of being at or below +2σ is 50% + (95%/2) = 97.5%.
Identify which exam domain this question belongs to, review the core concept, then practise similar questions from the same domain.
Read the scenario before looking for a memorised answer.
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Last reviewed: Jun 11, 2026
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