A café serves two types of drinks: Large, LLL, and Standard, SSS. The volumes, in ml, of Large drinks are distributed as L∼N(500,152)L \sim \text{N}(500, 15^2)L∼N(500,152) and Standard drinks are distributed as S∼N(330,82)S \sim \text{N}(330, 8^2)S∼N(330,82).
A Large drink and a Standard drink are selected at random.
Find the probability that the volume of the Large drink is less than 150% of the volume of the Standard drink.
Two Standard drinks are chosen at random.
Find the probability that their volumes differ by more than 10 ml.
The café sells drinks in trays. Each tray contains either 4 Large drinks or 6 Standard drinks. The weight of an empty tray, TTT, is distributed as T∼N(100,52)T \sim \text{N}(100, 5^2)T∼N(100,52). We assume 1 ml of drink weighs 1 g.
Find the probability that a tray of 6 Standard drinks weighs more than a tray of 4 Large drinks.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 439 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
