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The Normal Distribution

Overview

The Bell Curve.

What is it?

A symmetrical probability distribution where most data clusters around the mean.

History

Gauss derived this curve to handle errors in astronomical observations.

Key Idea

68-95-99.7 Rule.

Practice This Topic

Concept Guide

Plain English: In nature, extreme things are rare. Most people are average height. A few are tiny, a few are giants. When you plot this, it looks like a bell. The width of the bell is the Standard Deviation.

Real-world example: Manufacturing. Companies use the bell curve to decide which products to reject (Sigma ratings).

How to do it

  1. Identify the Mean (center).
  2. Identify Standard Deviation (step size).
  3. 68% of people are within 1 step (up or down).
  4. 95% are within 2 steps.
  5. 99.7% are within 3 steps.
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Common Pitfall

Applying it to things that aren't normal. Wealth distribution is NOT a bell curve (it's a Power Law).

Word Problem
"Average IQ is 100. SD is 15. What % of people are between 85 and 115?"
Reasoning: 85 is one step down. 115 is one step up. The rule says 68% of people fall in this range.

Practice Examples

The Bell
_--_ _/ \_ -1 μ +1
μ is Mean. +/-1 is Std Dev.