Your question is about finding the value of x such that the probability of completing the project in x weeks or less corresponds to a certain confidence level, given:
- Critical path duration (mean) = 20 weeks
- Standard deviation = 4 weeks
However, you didn't specify the probability or confidence level (e.g., 50%, 84%, 95%, etc.) for which you want to find x.
How to find x given a probability
Assuming the project duration follows a normal distribution (which is common in project management for critical path analysis), the formula to find x for a given cumulative probability P is:
x=μ+z×σx=\mu +z\times \sigma x=μ+z×σ
Where:
- μ=20\mu =20μ=20 weeks (mean duration)
- σ=4\sigma =4σ=4 weeks (standard deviation)
- zzz = z-score corresponding to the cumulative probability PPP
Example values of x for common probabilities
Probability (P)| z-score| x = 20 + z*4 (weeks)
---|---|---
50%| 0| 20
84%| +1| 24
97.5%| +2| 28
99.7%| +3| 32
16%| -1| 16
2.5%| -2| 12
What you should do next
- If you have a specific probability (e.g., "there is a 90% chance the project will be completed in x weeks or less"), provide that probability.
- I can then calculate the exact value of x for you.
If you want me to pick the most common confidence level (like 95%), then:
- For 95% probability, z≈1.645z\approx 1.645z≈1.645
- So, x=20+1.645×4=20+6.58=26.58x=20+1.645\times 4=20+6.58=26.58x=20+1.645×4=20+6.58=26.58 weeks
Rounded, x ≈ 27 weeks. Please provide the probability or confidence level if you want a precise answer!
