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

`\sigma_z = 10`

Step-by-step 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 = √(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 = √(Var(x) + Var(y))`

`\sigma_z = √(64 + 36)`

`\sigma_z = √(100)`

`\sigma_z = 10`