Normal Distribution: P(Z ≤ 0) — The Mean
P(Z ≤ 0) = 0.5000, confirming that exactly 50% of normally distributed values fall below 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.
Verify that the cumulative normal distribution probability at z = 0 is exactly 0.5, since the mean splits a symmetric normal distribution in half.
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.