Normal Distribution

The normal distribution is a bell-shaped, symmetric curve that describes how many real-world quantities are distributed. It is centred on the mean $\mu$ and its spread is controlled by the standard deviation $\sigma$.

Key features:

• Symmetric around the mean
• The mean, median, and mode are all equal
• Most values cluster near the centre; extreme values become increasingly rare

The 68–95–99.7 rule (empirical rule):

• About 68% of values fall within $1\sigma$ of the mean
• About 95% fall within $2\sigma$
• About 99.7% fall within $3\sigma$