若\(X\sim N(\mu,\sigma^2)\)，则其分布函数\(F_X(x)=P\{X\le x\}=P\left\{\dfrac{X-\mu}{\sigma}\le \dfrac{x-\mu}{\sigma}\right\}\)，而\(\dfrac{X-\mu}{\sigma}\sim N(0,1)\)，于是\(F_X(x)=\varPhi(\dfrac{x-\mu}{\sigma})\).