Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Each year, a transport company consumes $X$ litres of gasoline and $Y$ litres of diesel fuel, with $X$ and $Y$ independent and distributed as $X \sim N(10\,700,\,950^2)$ and $Y \sim N(13\,400,\,1210^2)$.
(a)[5]
Determine the probability that, in a randomly selected year, the firm's gasoline usage exceeds its diesel usage.
(b)[5]
The unit prices for gasoline and diesel fuel are $\$0.80$ and $\$0.85$ respectively. Find the probability that the combined cost of gasoline and diesel fuel in a randomly selected year lies between $\$20\,000$ and $\$22\,000$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct mean $E(X-Y)=10700-13400=-2700$” …