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.