Normal Distribution: P(Z ≤ −1.645)
P(Z ≤ −1.645) ≈ 0.05, meaning only 5% of values fall below this point, used as the one-tailed 95% significance threshold.
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 normal probability for z = −1.645, the critical value for one-tailed hypothesis tests at the 5% significance level.
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.