Answer
a. $0.0038$
b. $0.0228$
c. $0.5$
d. $0.3217$
Work Step by Step
Given $\mu=48,\sigma=3$, use Table E or a calculator:
a. $z1=\frac{36-48}{3}=-4, z2=\frac{40-48}{3}=-2.6667$
$P(36\lt X\lt 40)=P(z2)-P(z1)=0.0038-0=0.0038$
b. $z3=\frac{42-48}{3}=-2, P(X\lt 42)=P(z3)=0.0228$
c. $z4=\frac{48-48}{3}=0, P(X\gt48)=1-P(z4)=1-0.5=0.5$
d. $z5=\frac{43-48}{3}=-1.6667, z6=\frac{47-48}{3}=-0.3333$
$P(43\lt X\lt 47)=P(z6)-P(z5)=0.3695-0.0478=0.3217$
