Normal Distribution

Normal Distribution turns the famous bell curve into a clean, hands-on app: how do continuous values spread around an average, and how likely is any range of outcomes?

Whether you're a student meeting the topic for the first time, revising for an exam, or a teacher who needs a clear demo, this app keeps the focus on understanding — no clutter, no sign-up, no fuss.

WHAT YOU CAN DO

- Concept — A plain-language explanation of the normal distribution, its density function, the meaning of μ and σ, z-scores, and the 68–95–99.7 rule, with formulas rendered cleanly.

- Calculator — Set the mean μ, the standard deviation σ, and a value x, then instantly see P(X ≤ x), P(X > x), the z-score, the density f(x), and the summary statistics.

- Chart — Visualize the shape. Switch between the bell-shaped PDF and the S-shaped CDF, then slide μ to move the curve and change σ to widen or narrow it.

- Simulation — Draw a single value from the curve, or draw 500 at once and watch the histogram fill in the bell while the average and spread approach μ and σ (the law of large numbers in action).

- Examples — Three worked, real-world problems — adult heights, IQ scores, and packaging weights — that show exactly how to apply z-scores.

WHY THIS DISTRIBUTION MATTERS

The normal distribution is everywhere: heights, test scores, measurement errors, and — thanks to the Central Limit Theorem — the averages and sums of almost anything. Mastering it unlocks z-scores, confidence intervals, and most of inferential statistics.

Convention used: X is continuous, so areas under the curve give probabilities.
f(x) = 1 / (σ√(2π)) · e^(−(x − μ)² / (2σ²))
Mean = μ Variance = σ² z = (x − μ) / σ

BUILT TO BE SIMPLE
- Lightweight and fast.
- Clear, distraction-free interface.
- Interactive sliders and live results — learn by doing.

Note: an internet connection is used to display the formulas and ads.

Master the normal distribution by seeing it, computing it, and simulating it — all in one place.