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.
390 exam-style questions on AQA A Level Maths 2.4 N: Statistical distributions, covering 2.4.1 Discrete distributions and the binomial, 2.4.2 The Normal distribution (A-level only), and 2.4.3 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.