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

$p(13\leq x\leq16)=.1525$

$z=\frac{x-\mu}{\sigma}=\frac{13-11}{2}=1$ $z=\frac{x-\mu}{\sigma}=\frac{16-11}{2}=2.5$ $p(13\leq x\leq16)=p(1\leq z\leq2.5)=p(0\leq z\leq2.5)-p(0\lt z\leq1)=p(0\lt z\leq2.5)-p(0\lt z\leq.5)=.4938-.3413=.1525$ According to Table IV, page 773: $p(0\lt z\leq1)=.3413$ $p(0\lt z\leq2.5)=.4938$