Normal Distribution: P(Z ≤ 2.0)
P(Z ≤ 2.0) = 0.9772, so about 97.7% of normally distributed values fall below two standard deviations above the mean.
How to use this tool
- Enter z-score in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your p(z ≤ z) — cumulative probability and the full breakdown beneath it.
Look up the cumulative probability for z = 2.0, a key benchmark in statistics and quality control (the 2-sigma boundary).
Frequently asked questions
- What does Φ(z) represent?
- Φ(z) is the cumulative distribution function of the standard normal distribution — the probability that a standard normal random variable is less than or equal to z. For example, Φ(1.96) ≈ 0.975, corresponding to the 95% confidence interval.