Answer
a) $99.88$%
b) $98.9$%
c) $59.5$ to $73.4$ inches
Work Step by Step
a) We first must find the $z$-scores for each of the ends of the range:
$\frac{56−63.8}{2.6}=-3.0$
$\frac{75−63.8}{2.6}=4.3$
Using a table of $z$-scores and subtracting the two $z$-scores, we can find that $100(1−0.0012)=99.88$ % of women are in this range.
b) We use the same process for men:
$\frac{56−69.5}{2.4}=−5.625$
$\frac{75−69.5}{2.4}=2.29$
Using a table of $z$-scores and subtracting the two $z$-scores, we can find that
$98.9$ % of men are in this range.
c) Using a table of $z$-scores, we can find that $z=±1.65$. We now consider the tallest men and the shortest women to get:
$max=(1.65)(2.4)+69.5=73.4$ in
$min=−(1.65)(2.6)+63.8=59.5$ in
