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

Exam questions on Linear combinations of Normal random variables

1. The time $X$ minutes that a student takes to complete the first section of a test is modelled by $\mathrm{N}(20,4^2)$. The time $Y$ minutes taken to complete the second section is modelled by $\mathrm{N}(15,3^2)$. $X$ and $Y$ are independent.
   Find the probability that the first section takes longer than the second.2 marks
2. The random variables $X$ and $Y$ are independent, with $X\sim\mathrm{N}(12,3^2)$ and $Y\sim\mathrm{N}(7,2^2)$.
   Find $\mathrm{P}(3X-2Y>30)$.2 marks
3. Four adult passengers, chosen at random, ride in a lift. The mass of an adult passenger is modelled by $\mathrm{N}(75,12^2)$ kg and the mass of the luggage that one passenger carries by $\mathrm{N}(18,5^2)$ kg. All the masses are independent. A calculator may be used.
   Find the probability that the total mass of the four passengers, without their luggage, exceeds $320$ kg.3 marks