Chapter 5 - Continuous Random Variables - Exercises 5.73 - 5.92 - Learning the Mechanics - Page 256: 5.79b

$P(40\leq x\leq50)=.5236$

$q=1-p=1-.40=.60$ $\mu=np=100(.40)=40$ $\sigma=\sqrt {npq}=\sqrt {100(.40)(.60)}=4.90$ $z=\frac{(39+.5)-40}{4.90}=-.10$ $z=\frac{(50+.5)-40}{4.90}=2.14$ $P(40\leq x\leq50)=P(x\leq50)-P(x\leq39)=P(z\leq2.14)-P(z\leq-.10)=P(0\leq z\leq2.14)+P(0\leq z\leq.10)=.4838+.0398=.5236$