# Question: For a freshman taking introductory statistics and majoring in psychology

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 μX = 22.7, σ2x = 17.64, μY = 22.7, σ2Y = 12.25, and ρ = 0.78.

(a) Find P(18.5 < Y < 25.5).

(b) Find E(Y | x).

(c) Find Var(Y | x).

(d) Find P(18.5 < Y < 25.5 | X = 23).

(e) Find P(18.5 < Y < 25.5 | X = 25).

(f) For x = 21, 23, and 25, draw a graph of z = h(y | x) similar to Figure 4.5-1.

(a) Find P(18.5 < Y < 25.5).

(b) Find E(Y | x).

(c) Find Var(Y | x).

(d) Find P(18.5 < Y < 25.5 | X = 23).

(e) Find P(18.5 < Y < 25.5 | X = 25).

(f) For x = 21, 23, and 25, draw a graph of z = h(y | x) similar to Figure 4.5-1.

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