Combining random variables

A vending machine that serves coffee pours a varying amount of liquid into a cup with varying mass. Assume that the masses of the liquid and the cup are independent.

Here are summary statistics for the masses of the liquid and the cups:

	Mean	Standard deviation
Liquid	$μ_{L} = 250 g$ ‍	$σ_{L} = 20 g$ ‍
Cup	$μ_{C} = 150 g$ ‍	$σ_{C} = 10 g$ ‍

Let

T =

the total mass of a randomly selected cup filled with liquid from this machine.

What is the standard deviation of $T$ ‍?

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 8

Problem