Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
In each month, the company sells $X$ kg of brown sugar and $Y$ kg of white sugar, with $X$ and $Y$ having the independent distributions $N(2500, 120^2)$ and $N(3700, 130^2)$ respectively.
(a)[3]
Determine the mean and standard deviation of the total quantity of sugar sold by the company in $3$ randomly selected months.
(b)[5]
The company earns a profit of $\$1.50$ for each kilogram of brown sugar sold and incurs a loss of $\$0.20$ for each kilogram of white sugar sold. Find the probability that, in a randomly selected month, the overall profit is below $\$3000$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct mean $= 3(2500 + 3700) = 18600$” …