Normal Distribution Calculator
Calculate z-score, probability density, cumulative probability, and right-tail probability for a normal distribution using a value, mean, and standard deviation.
Formulae used:
z = (x − μ) / σ
PDF = (1 / (σ√(2π))) · e^(-(1/2)z²)
| Metric | Value |
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Privacy: calculations run locally in your browser. No inputs are stored or transmitted.
How it works
This tool standardizes the value with a z-score, then estimates the normal CDF using a numerical approximation of the error function.
Examples
- x = 85, μ = 70, σ = 10 → z = 1.5
- Left-tail probability is P(X ≤ x)
- Right-tail probability is P(X > x)
FAQ
- What does this normal distribution calculator compute?
It computes z-score, probability density (PDF), cumulative probability to the left of x (CDF), and right-tail probability for a normal distribution.
- What is z-score?
A z-score tells you how many standard deviations a value is above or below the mean.
- What happens if standard deviation is 0?
The calculation is undefined because a normal distribution requires a positive standard deviation.
- Are calculations stored?
No. Everything runs locally in your browser.