This is obvious from a picture. If f(x) is the the p.d.f. of X and ϕ(x) is the p.d.f. of the standard normal distribution, then f(x) is ϕ(x) shifted μ to the right. Therefore, the area under f(x) up to 0 is the same as the area under ϕ(x) up to -μ. More formally, f(x) = ϕ(x - μ), so
In general, if F(x) is a c.d.f. of a normal distribution with mean μ and deviation σ, then .