Mathematics 9709 · AS & A Level · Linear combinations of random variables

Linear combinations of random variables — practice question

For large and small cups of tea, the volumes in millilitres are represented by the distributions $N(200, 30)$ and $N(110, 20)$, respectively.
(a)[4]

Find the probability that the combined volume of a randomly chosen large cup of tea and a randomly chosen small cup of tea is less than $300$ ml.

(b)[6]

Find the probability that the volume of a randomly chosen large cup of tea is more than twice the volume of a randomly chosen small cup of tea.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Recognition of distribution $N(310, 50)$.

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