Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The weights, in kilograms, of large sacks and small sacks of flour are distributed as $N(55, 3^2)$ and $N(27, 2.5^2)$ respectively.
(a)[5]
Several sacks are placed on a boat. The greatest load of flour that the boat is able to carry safely is $340\,\text{kg}$. Find the probability that the boat can carry safely $3$ randomly chosen large sacks of flour and $6$ randomly chosen small sacks of flour.
(b)[5]
Determine the probability that the mass of a randomly chosen large sack of flour is greater than the total mass of two randomly chosen small sacks of flour.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The mean is correct: $E(T)=3\times55+6\times27=327$.” …