Answer
a. $0.0013$
b. $0.5$
c. $0.0082$
d. $0.5511$
Work Step by Step
Given $\mu=3years=36month,\sigma=4months$, use table E or a calculator:
a. $z1=\frac{4\times12-36}{4}=3, P(X\gt 48)=1-P(z1)=1-0.9987=0.0013$
b. $z2=\frac{3\times12-36}{4}=0, P(X\lt36)=P(z2)=0.5$
c. $z3=\frac{3.8\times12-36}{4}=2.4, z4=\frac{4.5\times12-36}{4}=4.5$
$P(3.8\lt X\lt3.5years)=P(4)-P(z3)=1-0.9918=0.0082$
d. $z5=\frac{2.5\times12-36}{4}=-1.5, z6=\frac{3.1\times12-36}{4}=0.3$
$P(2.5\lt X\lt3.1years)=P(z6)-P(z5)=0.6179-0.0668=0.5511$
