Chapter 5 - Continuous Random Variables - Exercises 5.20 - 5.52 - Learning the Mechanics - Page 242: 5.32d

$x=16.84$

$p(z\gt z_0)=.95$ ($z_0$ is negative) $p(z\gt z_0)=p(z_0\lt z\leq0)+p(z\gt0)=p(0\leq z\lt-z_0)+.5=.95$ $p(0\lt z\lt -z_0)=.95-.5=.45$ According to Table IV, page 773: If $p(0\lt z\lt -z_0)=.45$ then $-z_0\approx1.645$ $z_0\approx-1.645$ $z_0=\frac{x-\mu}{\sigma}$ $-1.645=\frac{x-30}{8}$ $x-30=-1.645(8)$ $x=30-13.16=16.84$