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

Linear combinations of random variables — practice question

The masses, measured in kilograms, of the large bags and the small bags of potatoes are independently distributed as $N(2.5, 0.05)$ and $N(0.8, 0.02)$ respectively.
(a)[5]

Determine the probability that the combined mass of one randomly selected large bag of potatoes and one randomly selected small bag of potatoes exceeds $3.55\text{ kg}$.

(b)[5]

Find the probability that the mass of a randomly chosen large bag of potatoes is less than $3$ times the mass of a randomly chosen small bag of potatoes.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Thus $N(2.5+0.8,\ 0.05+0.02)=N(3.3,0.07)$

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