Answer:
D
Step-by-step explanation:
Since 2 variables are inter-dependent (there is correlation between them given as 0.64), we need to use the formula shown below:
Var(x+y) = Var(x) + Var(y) + 2 * correlation coefficient * [tex]\sqrt{Var(x)}[/tex] * [tex]\sqrt{Var(y)}[/tex]
Given Var(m) = 1600, Var(n) = 900 and correlation coefficient 0.64, we plug them into the formula and solve:
Var (m+n) = Var(m) + Var(n) + 2 * correlation coefficient * [tex]\sqrt{Var(m)}[/tex] * [tex]\sqrt{Var(n)}[/tex]
= 1600 + 900 + 2(0.64)*Sqrt(1600)*Sqrt(900)
= 4036
correct answer d
