Answer:
4
Explanation:
Given that:
X = time taken to complete mathematics homework
Y= time taken to complete language homework
Standard deviation of X ; SD(X) = 3
Standard deviation of Y ; SD(Y) = 4
rho = - 0.375
rho = Cov(X, Y) / SD(X) * SD(Y)
-0.375 = COV(X, Y) / 3 * 4
COV(X, Y) = 12 * - 0.375
COV(X,Y) = - 4.5
Variance(X, Y) = V(X, Y)
V(X, Y) = V(X) + V(Y) + 2COV(X,Y)
V(X) =SD(X)² = 3² = 9
V(Y) = SD(Y)² = 4² = 16
V(X,Y) = 9 + 16 + 2(-4.5)
V(X, Y) = 16
SD(X, Y) = sqrt(V(X, Y)) = sqrt(16) = 4
Hence, standard deviation to complete entire homework, SD(X, Y) = 4