Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The independent distributions of the masses, measured in kilograms, of large sacks of flour and small sacks of flour are $N(40, 1.5^2)$ and $N(12, 0.7^2)$ respectively.
(a)[4]
Calculate the probability that the total mass of 6 randomly selected large sacks of flour exceeds $245\text{ kg}$.
(b)[6]
Calculate the probability that the mass of a randomly selected large sack of flour is less than $4$ times the mass of a randomly selected small sack of flour.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Distribution: $N(240, 6\times1.5^2)$ or $N(240, 13.5)$” …