PMP Process — Managing Technical Aspects Practice Question
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?
⚠ Common exam trap
Many candidates confuse 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%.
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
✓
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%.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✓
97.5%
Why this is correct
This option correctly represents the cumulative probability of completing the project at or before a duration that is two standard deviations above the mean. In a standard normal distribution, approximately 95% of data falls within ±2 standard deviations from the mean. This leaves 2.5% of outcomes in the lower tail (below -2 SD) and 2.5% in the upper tail (above +2 SD). Therefore, the probability of completing at or below +2 standard deviations is 100% minus the upper 2.5% tail, resulting in 97.5%.
- ✗
95%
Why it's wrong here
This option refers to the probability of project completion falling *within* two standard deviations of the mean, encompassing both earlier and later completion times. While 95% of outcomes lie between -2 and +2 standard deviations in a normal distribution, this represents a two-sided interval centered on the mean. It does not accurately reflect a one-sided cumulative probability of completing the project *at or below* a specific upper limit, which is typically what stakeholders are interested in for a target completion date.
- ✗
84%
Why it's wrong here
This option corresponds to the cumulative probability of completing the project at or before a duration that is one standard deviation above the mean. In a normal distribution, approximately 34% of outcomes fall between the mean and +1 standard deviation. Adding this to the 50% of outcomes that fall below the mean yields 84%. While a valid probability for a Z-score of +1, it does not align with the higher confidence level (and thus higher Z-score) indicated by the correct answer for this scenario.
- ✗
68%
Why it's wrong here
This option represents the probability of project completion occurring *within* one standard deviation of the mean, covering both positive and negative deviations. This interval, from -1 to +1 standard deviation, accounts for approximately 68% of all possible outcomes in a normal distribution. However, it describes a symmetrical range around the mean rather than a cumulative probability up to a specific upper threshold, making it unsuitable for determining the likelihood of completing by a target date that is two standard deviations above the mean.
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Written by Johnson Ajibi, MSc IT Security
Senior Network & Security Engineer · founder of Courseiva
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