Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The masses, measured in kilograms, of large and small bags of potatoes follow the independent distributions $N(2.5, 0.05)$ and $N(0.8, 0.02)$ respectively.
(a)[5]
Find the probability that the combined mass of a randomly chosen large bag of potatoes and a randomly chosen small bag of potatoes is greater than $3.55\text{ kg}$.
(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: “By adding the means and variances, $N(2.5+0.8,0.05+0.02)=N(3.3,0.07)$” …