Normal Distribution: P(Z ≤ 1.96)
P(Z ≤ 1.96) = 0.9750, meaning 97.5% of values in a standard normal distribution fall below a z-score of 1.96.
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.
Find the cumulative probability for z = 1.96, the critical value used in 95% confidence intervals, using the standard normal distribution.
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.