Answer
a. $0.0668$
b. $0.0228$
c. $0.4649$
d. $0.0934$
Work Step by Step
Given $\mu=53,\sigma=4$, use table E or a calculator:
a. $z1=\frac{59-53}{4}=1.5, P(X\gt 59)=P(z\gt z1)=1-P(z1)=1-0.9332=0.0668$
b. $z2=\frac{45-53}{4}=-2, P(X\lt45)=P(z\lt z2)=P(z2)=0.0228$
c. $z3=\frac{50-53}{4}=-0.75, z4=\frac{55-53}{4}=0.5,
P(50\lt X\lt 55)=P(z3\lt z\lt z4)=P(z4)-P(z3)=0.6915-0.2266=0.4649$
d. $z5=\frac{58-53}{4}=1.25, z6=\frac{62-53}{4}=2.25,
P(58\lt X\lt 62)=P(z5\lt z\lt z6)=P(z6)-P(z5)=0.9878-0.8944=0.0934$
