Answer :
We have to write the formula of the height H of a boy in function of the father's height (D) and the mother's height (M) using the mid-parent rule.
The opposite gender for the boy will be its motehr gender. Then, the mother's height will be multiplied by the factor 12/13 before averaging with the father's height.
Then, we can write the corrected mothers height as:
[tex]M^{\prime}=\frac{12}{13}M[/tex]Then, averaging both heights (father's heigth D and corrected mother's height M'), we get:
[tex]\begin{gathered} H=\frac{D+M^{\prime}}{2} \\ H=\frac{1}{2}(D+\frac{12}{13}M) \\ H=\frac{D}{2}+\frac{12}{2\cdot13}M \\ H_{\text{boy}}=\frac{D}{2}+\frac{6}{13}M \end{gathered}[/tex]In the case of a girl's adult height, we change the opposite gender so the father's heihgt is affected by the factor.
Then, the height of the girl will be:
[tex]\begin{gathered} H=\frac{1}{2}(D^{\prime}+M) \\ H=\frac{1}{2}(\frac{12}{13}D+M) \\ H_{\text{girl}}=\frac{6}{13}D+\frac{M}{2} \end{gathered}[/tex]Answer:
a) The boy's height will be H = (1/2)*D + (6/13)*M
b) The girl's height will be H = (6/13)*D + (1/2)*M
