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Normal Distribution Sample Generator

Generates a random sample from a normal (bell-curve) distribution centred on 50 with a standard deviation of 15, computed with the Box–Muller transform and clamped to a 0–100 range, for teaching what a normal distribution looks like or for demo/placeholder statistical data.

What this generator does

Draws a sample from a normal distribution rather than a uniform one, so values cluster around the mean and thin out towards the tails — the shape most natural measurements follow.

How to use this tool

  1. Press generate for a normal-distribution sample.

Worked examples

Shape
About 68% of draws fall within one standard deviation of the mean, about 95% within two

Common use cases

  • Teaching what a normal distribution looks like
  • Demo/placeholder statistical data
  • Quick statistics examples

How this generator works

Two independent uniform random numbers are combined by the Box–Muller transform into a value following a standard normal curve, which is then scaled to a mean of 50 and a standard deviation of 15 and clamped to the 0–100 range. The clamp is the one departure from a true normal distribution: values that would otherwise fall outside 0 or 100 pile up at whichever boundary they crossed instead of extending past it.

Limitations and good to know

  • A small number of draws will not look like a bell curve. The shape only becomes visible over many samples.

A teaching/demo tool, not a statistically rigorous simulation or research-grade random-variate generator.

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