Hi, I need help with solving part b of this problem and making sure I did part a right. I attached the problem and my solution. Thank you!

" ) P ( D 7 100 ) b 3 a ) x -7 Mom's height in S.U. Y -7 Daughter's height in S.U. Y= P X + VI - p2 2 ; p = 0.5 Y E (DIX = X ) = px = 0.5x var ( Y 1 X = x ) = var ( p x + VI -p2 z / x = x ) = var ( px + VI-p2, z ) = var ( p x ) + var( VI- p2 z ) var (z ) = 1 bc Zis pX is a constant = 1 + ( 1 - p2 ) var (z ) -> standard normal sovar = 0 L\f3. Heights of Mothers and Daughters The heights of a population of mother-daughter pairs have a bivariate normal distribution with correlation 0.5. a] (If the mothers on the 90th percentile of mothers' heights. what proportion have daughters who are taller than the 90th percentile of daughters' heights? h} In what proportion of mother-daug hter pairs are both women taller than average? [This means the mothers are taller than the average mother and the daughters are taller than the average daughter.) [Hint: Remember that you can express standard bivan'ate normal variables in terms of two independent standard normal variables]