Quick Answer: The normal distribution (bell curve) is a symmetrical probability distribution where most data points cluster around the average, and taper off equally on both sides. Human height, blood pressure, IQ scores, and measurement errors all naturally follow this mathematically perfect curve.
The 68-95-99.7 Rule (The Empirical Rule)
The normal distribution is defined by two numbers: the mean (the center average) and the standard deviation (how spread out the data is). The curve follows a strict mathematical rule:
- 68% of the data falls within 1 standard deviation of the mean.
- 95% of the data falls within 2 standard deviations.
- 99.7% of the data falls within 3 standard deviations.
Real-World Example: Men's Height
In the US, the average adult male height is about 70 inches (5'10"), with a standard deviation of 3 inches. Because height is normally distributed:
- 68% of men are between 67" and 73" (5'7" to 6'1")
- 95% of men are between 64" and 76" (5'4" to 6'4")
- A man who is 6'7" (79 inches) is 3 standard deviations above the mean. Only 0.15% of men are this tall or taller.
Why is it Everywhere?
Why does nature love the bell curve? Additive processes. Your final height is the sum of thousands of tiny, independent genetic and environmental factors. When you add up many independent random variables, their sum converges into a normal distribution (thanks to the Central Limit Theorem). Any trait in nature created by the addition of many small effects will form a bell curve.
Not Everything is Normal
While biology loves normal distributions, human economics often does not. Wealth distribution follows a Power Law (the Pareto Principle or 80/20 rule), where a tiny fraction of the population holds the vast majority of wealth. Applying bell curve math to power-law domains (like finance) caused the 2008 financial crisis.