The Normal Distribution

• The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution with a bell-shaped curve.
• The curve is symmetric around the mean value.
• The distribution is defined by the mean (μ), which represents the centre of the curve, and the standard deviation (σ), which measures the spread of data points.
• Mathematically, the probability density function of a normal distribution is given by a specific formula.
• The distribution is used across various fields such as statistics, natural sciences, and social sciences.
• A key property is the Central Limit Theorem, which says that the sum of many independent, identically distributed variables approximates a normal distribution, regardless of the individual variables’ distribution.
• The empirical rule (68-95-99.7 rule) states that within a normal distribution, roughly 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three.