Normal Distribution Calculator
Compute Z-score, percentile rank, and tail probabilities for any normally distributed value. Visualize the bell curve with the relevant area shaded.
Inputs
Advertisement
Result
Bell curve (shaded tail)
"95% confidence" doesn't mean what you think
A common misuse: treating Z=1.96 (≈ 95th percentile two-tailed) as a "5% chance of error" on a specific experiment. It isn't — it's the cutoff such that 95% of confidence intervals would contain the true parameter under repeated sampling. The probability that your specific interval contains the truth is either 0 or 1, you just don't know which.
Who uses it
- Students doing t-tests, hypothesis tests, etc.
- Analysts checking outlier classifications.
- Educators illustrating the 68-95-99.7 rule with real numbers.
Limitations
- Assumes the input is actually normally distributed. For long-tailed data (income, city size), this is wrong.
- Doesn't replace Confidence Interval — that tool estimates μ and σ from your sample.