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Find the probability that, on a chosen day, $Y$ is smaller than the combined total of $W$ and $X$.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
At the gym each day, Sarah runs three times. The three run distances, measured in metres, are independently distributed as $W \sim \mathcal{N}(1520, 450)$, $X \sim \mathcal{N}(2250, 720)$ and $Y \sim \mathcal{N}(3860, 1050)$.