If $X,Y,Z$ are independent standard normal random variables, compute P(3X+2Y<6Z-7).
One way is to evaluate $\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{(6z-2y-7)/3}\frac{\exp(-(x^2+y^2+z^2)/2)}{2\pi\sqrt{2\pi}}dxdydz.$ But I don't know how to calculate this.