Normal Distribution The graph below is the density function of a normally distributed random variable with expected value μ (mu) and standard deviation σ (sigma). By moving the scroll bars you can change the values of μ and σ. The blue vertical line gives the location of the expected value and the red horizontal line gives the interval (μ-σ, μ+σ). Thus, its length is twice the standard deviation (σ). The blue density function is the density function of the standard normal distribution.