Chapter 5 - Continuous Random Variables - Exercises 5.20 - 5.52 - Learning the Mechanics - Page 242: 5.31d

$p(7.8\leq x\leq12.6)=.7333$

$z=\frac{x-\mu}{\sigma}=\frac{7.8-11}{2}=-1.6$ $z=\frac{x-\mu}{\sigma}=\frac{12.6-11}{2}=.8$ $p(7.8\leq x\leq12.6)=p(-1.6\leq z\leq.8)=p(-1.6\leq z\leq0)+p(0\lt z\leq.8)=p(0\lt z\leq1.6)+p(0\lt z\leq.8)=.4452+.2881=.7333$ According to Table IV, page 773: $p(0\lt z\leq.8)=.2881$ $p(0\lt z\leq1.6)=.4452$