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# Combining random variables

AP.STATS: VAR‑5 (EU), VAR‑5.E (LO), VAR‑5.E.1 (EK), VAR‑5.E.2 (EK), VAR‑5.E.3 (EK)

## Problem

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:
MeanStandard deviation
Liquidmu, start subscript, L, end subscript, equals, 250, start text, g, end textsigma, start subscript, L, end subscript, equals, 20, start text, g, end text
Cupmu, start subscript, C, end subscript, equals, 150, start text, g, end textsigma, start subscript, C, end subscript, equals, 10, start text, g, end text
Let T, equals the total mass of a randomly selected cup filled with liquid from this machine.
What is the standard deviation of T?