← Apply probability distributions
4 The normal distribution
A continuous, symmetric bell curve described by its mean μ and standard deviation σ. Probabilities are areas under the curve. Standardising (z-score) z=\frac{x-\mu}{\sigma} How many standard deviations x is from the mean. Then use the standard normal (or calculator).The 68–95–99.7 rule
- ≈ 68% of data within 1σ of the mean.
- ≈ 95% within 2σ.
- ≈ 99.7% within 3σ.
- Use z-scores + calculator/tables for exact probabilities; use inverse-normal to go from a probability back to an x-value.