Chapter 5 - Continuous Random Variables - Exercises 5.20 - 5.52 - Learning the Mechanics - Page 242: 5.33b

$x=36.72$

$p(z\lt z_0)=.80=80$% $p(z\lt z_0)=p(z\leq0)+p(0\lt z\lt z_0)$ $p(0\lt z\lt z_0)=p(z\lt z_0)-p(z\lt 0)=.8-.5=.3$ According to Table IV, page 773: If $p(0\lt z\lt z_0)=.3$ then $z_0\approx.84$ $z_0=\frac{x-\mu}{\sigma}$ $.84=\frac{x-30}{8}$ $x-30=.84(8)$ $x=30+6.72=36.72$