Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
For large and small packets of Maxwheat cereal, the masses in grams are independently distributed as $N(410.0,\,3.6^2)$ and $N(206.0,\,3.7^2)$, respectively.
(a)[5]
Find the probability that a randomly selected large packet has a mass greater than twice the mass of a randomly selected small packet.
(b)[6]
The packets are packed into boxes, and all the boxes look identical. $60\%$ of the boxes contain exactly $10$ large packets chosen at random. The remaining $40\%$ contain exactly $20$ small packets chosen at random. Find the probability that a randomly selected box has packets whose total mass is more than $4080$ grams.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly taking $D=L-2S$, $E(D)=410-2(206)=-2$” …