Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The masses, measured in kilograms, of large sacks of grain and small sacks of grain follow the distributions $\mathrm{N}(53,11)$ and $\mathrm{N}(14,3)$ respectively.
(a)[5]
Find the probability that the mass of a randomly chosen large sack is greater than four times the mass of a randomly chosen small sack.
(b)[5]
A lift can safely carry a maximum mass of $1000\text{ kg}$. Find the probability that it can safely carry 12 randomly chosen large sacks together with 25 randomly chosen small sacks.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct mean value $E(D) = -3$” …