Answer
a) 46.8 percent
b) 98.8 percent
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:
$= \frac{64-63.8}{2.6}=.08$
$= \frac{77-63.8}{2.6}=5.077$
Using a table of z-scores and subtracting the two z-scores, we find that 46.8 percent 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 find that 98.8 percent of men are in this range.
c) Using a table of z-scores, we find that the value of z is $\pm1.9$. We now consider the tallest men and the shortest women to obtain:
$max=(1.9)(2.4)+69.5=74.06 \ in$
$min=-(1.9)(2.6)+63.8=58.86\ in$
