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

Linear combinations of random variables — practice question

The juice volumes, measured in litres, for large bottles and small bottles have distributions $N(5.10, 0.0102)$ and $N(2.51, 0.0036)$ respectively.
(a)[5]

Find the probability that the total juice volume in $3$ randomly selected large bottles and $4$ randomly selected small bottles is less than $25.5$ litres.

(b)[5]

Find the probability that a randomly chosen large bottle has a volume of juice at least twice that of a randomly chosen small bottle.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Find the mean as $E(3L+4S)=25.34$.

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