$4\mathrm{.}8\mathrm{.}2$ For the Gaussian $(0,1)$ complemen$-$

tary CDF $Q(z),$ a useful numerical approx$-$

imation for $z0$ is

hat$(Q)(z)=({\displaystyle \underset{n=1}{\overset{5}{}}}{a}_n{t}^n)e^{-\frac{z^2}{2}},$

where

$t,=\frac{1}{1+0\mathrm{.}231641888z}{a}_1=0\mathrm{.}127414796$

$a_2,=-0\mathrm{.}142248368,a_3=0\mathrm{.}7107068705$

$a_4,=-0\mathrm{.}7265760135,a_5=0\mathrm{.}5307027145.$

To compare this approximation to $Q(z),$ use

MATLAB to graph

$e(z)=\frac{Q(z)-(hat(Q))(z)}{Q(z)}.$