Answer to Question #282261 in Statistics and Probability for Mao

Question

ST.A distance is measured as 27.3 inches and 15.6 inches with the standard deviation (error) of 0.16 inches and 0.08 inches respectively. Determine the mean and the standard deviation of the sum. 

Answer 1

$X:u_x=27.3, σ_x=0.16$

$Y:u_y=15.6, σ_y=0.08$

$Z=X+Y\implies u_z=u_x+u_y=27.3+15.6=42.9, σ^2_z=σ^2_x+σ^2_y+2cov(x,y)$

Since there is no information provided to determine whether X and Y are dependent, then i assume it means they are not, so $σ^2_z=0.16^2+0.08^2=0.032\implies σ_z=\sqrt{0.032}\approx0.179$

So, $u_z=42.9, σ_z\approx0.179$