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Statistics and probability

Course: Statistics and probability > Unit 9

Lesson 4: Combining random variables

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)

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	mu, start subscript, L, end subscript, equals, 250, start text, g, end text	sigma, start subscript, L, end subscript, equals, 20, start text, g, end text
Cup	mu, start subscript, C, end subscript, equals, 150, start text, g, end text	sigma, 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?

(Choice A)
20, plus, 10 grams
(Choice B)
20, squared, plus, 10, squared grams
(Choice C)
square root of, 20, squared, plus, 10, squared, end square root grams
(Choice D)
It cannot be determined from the information given because the masses are not independent.

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Statistics and probability

Course: Statistics and probability > Unit 9

Problem