For a freshman taking introductory statistics and majoring
Chapter 4, Problem 6E(choose chapter or problem)
For a freshman taking introductory statistics and majoring in psychology, let \(X\) equal the student's ACT mathematics score and \(Y\) the student's ACT verbal score. Assume that \(X\) and \(Y\) have a bivariate normal distribution with \(\mu_{X}=22.7, \sigma_{X}^{2}=17.64, \mu_{Y}=22.7, \sigma_{Y}^{2}=12.25\), and \(\rho=0.78\).
(a) Find \(P(18.5<Y<25.5)\).
(b) Find \(E(Y \mid x)\).
(c) Find \(\operatorname{Var}(Y \mid x)\).
(d) Find \(P(18.5<Y<25.5 \mid X=23)\).
(e) Find \(P(18.5<Y<25.5 \mid X=25)\).
(f) For \(x=21,23\), and \(25\) , draw a graph of \(z=h(y \mid x)\) similar to Figure 4.5-1.
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