f[x_,σ_]=Exp[-x^2/2/σ^2]/Sqrt[2 Pi]/σ

Plot[f[x,1],{x,-4,4}]

Manipulate[Plot[f[x,σ],{x,-4,4},PlotRange->{0,4}],{σ,0.01,10}]

Plot[Erf[x],{x,-4,4}]