Normal distribution
Normal distribution is a symmetric, bell-shaped probability distribution described fully by its mean and standard deviation.
Also known asGaussian · bell curve
See it move
The infographic is a bell-curve chart with probability density on the vertical axis and standard deviations from the mean on the horizontal axis. The symmetric bell is centred on zero and annotated with the empirical rule: 68% of observations fall within ±1σ of the mean, 95% within ±2σ, and 99.7% within ±3σ.
The formula
Variables
- Standard normal variable
- Observed value of the normally distributed variable
- Population mean of the distribution
- Population standard deviation of the distribution
Standardizing converts any N(μ, σ²) variable to a standard normal Z ~ N(0, 1) so z-tables can be used directly.
Check yourself
Customer waiting times at a service centre are normally distributed with a mean of 8 minutes and a standard deviation of 2 minutes. Approximately what proportion of customers wait between 4 minutes and 12 minutes?