The Normal Distribution, N(μ,σ²)

The normal distribution is described by two parameters: the mean (μ) and the variance (σ²). In this app you can explore how changing these parameters affects the shape of the curve.

The standard normal distribution, shown in grey, has a μ of 0 and a σ² of 1.

For the standard normal distribution, 68.26% of all values fall within the interval [-1,1] and 95.44% within the interval [-2,2]. If our variable of interest is not standardised, we can still make statements such as: “65% fall within [μ-1σ, μ+1σ], 95.44% fall within [μ-2σ, μ+2σ]”. In this case, the boundaries of the interval change according to μ and σ.