Chapter 5 - Continuous Random Variables - Exercises 5.20 - 5.52 - Applying the Concepts - Basic - Page 243: 5.43b

$p(400\lt x\lt500)=.1508$

$z=\frac{x-\mu}{\sigma}=\frac{500-605}{185}=-.57$ $z=\frac{x-\mu}{\sigma}=\frac{400-605}{185}=-1.11$ According to table IV, page 773: $p(0\lt z\lt1.11)=.3665$ $p(0\lt z\lt.57)=.2157$ $p(400\lt x\lt500)=p(-1.11\lt z\lt-.57)=p(-1.11\lt z\lt0)-p(-.57\lt z\lt0)=p(0\lt z\lt1.11)-p(0\lt z\lt.57)=.3665-.2157=.1508$