Question

Assume X and Y are indepndent. Assume that X has mean 10 and standard deviation 8. Assume Y has mean 12 and standard deviation 6. What is the standard deviation of the variable Z = X + Y. a. 8 b. 6 c. 10 d. 12

Answer 1

Answer:

$\sigma_z = 10$

Explanation:

Given

$\bar x = 10$

$\sigma_x = 8$

$\bar y = 12$

$\sigma_y = 6$

$z = x + y$

Required

$\sigma_z$

This is calculated as:

$\sigma_z = \sqrt{Var(x) + Var(y)}$

Calculate $Var(x)$

We have:

$Var(x) = \sigma_x^2$

$Var(x) = 8^2$

$Var(x) = 64$

Calculate $Var(y)$

We have:

$Var(y) = \sigma_y^2$

$Var(y) = 6^2$

$Var(y) = 36$

So, we have:

$\sigma_z = \sqrt{Var(x) + Var(y)}$

$\sigma_z = \sqrt{64 + 36}$

$\sigma_z = \sqrt{100}$

$\sigma_z = 10$