#### Answer

a) $23.32$ inches
b) This works for most people.

#### Work Step by Step

a) We can find that the z-score that corresponds to this is $1.6$. Hence, it follows: $(1.6)(1.2)+21.4=23.32.$
Women are generally shorter, so when determining the minimum height, we do not have to worry about the height of women.
b. We find the z-scores for the genders: $z_{men}=\frac{23.5−21.4}{1.2}=1.75$
$z_{women}=\frac{23.5−19.6}{1.1}=3.55$.
Using a z-table, we can see that more than $95$ percent of men and around $99.99$ percent of women will fit, so this works for most people.