Answer
a) $46.8$ %
b) $98.8$ %
c) Between $58.86$ and $74.06$ inches
Work Step by Step
a) We first must find the $z$-scores for each of the ends of the range:
$\frac{64−63.8}{2.6}=0.08$
$\frac{77−63.8}{2.6}=5.077$
Using a table of $z$-scores and subtracting the two $z$-scores, we can find that $46.8$ % of women are in this range.
b) We use the same process for men:
$\frac{64−69.5}{2.4}=−2.29$
$\frac{77−69.5}{2.4}=3.125$
Using a table of $z$-scores and subtracting the two $z$-scores, we can find that
$98.8$ % of men are in this range.
c) Using a table of $z$-scores, we can find that $z=±1.9$. We now consider the tallest men and the shortest women to get:
$max=(1.9)(2.4)+69.5=74.06$ in
$min=−(1.9)(2.6)+63.8=58.86$ in
