Chapter 5 - Continuous Random Variables - Exercises 5.20 - 5.52 - Applying the Concepts - Basic - Page 243: 5.42a

$p(illegal)=.4410$

$z=\frac{x-\mu}{\sigma}=\frac{60-55.7}{11.5}=.37$ $z=\frac{x-\mu}{\sigma}=\frac{40-55.7}{11.5}=-1.37$ According to table IV, page 773: $p(0\lt z\lt.37)=.1443$ $p(0\lt z\lt 1.37)=.4147$ $p(legal)=p(40\lt x\lt60)=p(-1.37\lt z\lt.37)=p(-1.37\lt z\lt0)+p(0\lt z\lt.37)=p(0\lt z\lt1.37)+p(0\lt z\lt.37)=.1443+.4147=.5590$ $p(illegal)=1-p(legal)=1-.5590=.4410$