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 OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.