Linear combinations of Normal random variablesEdexcel A-Level Further Maths: Mind map

Exam questions on Linear combinations of Normal random variables

1. The mass of an apple, $A$ g, is modelled by $A\sim N(150, 12^2)$ and the mass of a pear, $P$ g, by $P\sim N(200, 15^2)$. The masses of apples and pears are independent.
   Find the probability that a randomly chosen pear is heavier than a randomly chosen apple.2 marks
2. The independent random variables $X$ and $Y$ are distributed as $X\sim N(20, 3^2)$ and $Y\sim N(15, 2^2)$. The random variable $W=3X-2Y$.
   Find $\mathrm{P}(W<25)$.2 marks
3. The length of a metal rod, $X$ cm, is modelled by $X\sim N(50, 0.4^2)$. The lengths of different rods are independent.
   Two rods are chosen at random and placed end to end. Find the probability that their total length exceeds $100.5$ cm.3 marks