An agricultural scientist monitors the daily yield of milk, in litres, from a herd of cows at a local farm. The daily yield in the spring, S S\,S litres, can be modelled by a normal distribution S∼N(800,602)S \sim \text{N}(800, 60^2)S∼N(800,602).
Using standardisation and showing your working, find the probability that, on a randomly selected day in the spring,
(i) more than 710 litres of milk is produced,
(ii) 800 litres of milk, correct to the nearest 40 litres, is produced.
The daily milk yield in the winter, W W\,W litres, can be modelled by W∼N(μ,σ2)W \sim \text{N}(\mu, \sigma^2)W∼N(μ,σ2).
Given that P(W>745)=0.1056\text{P}(W > 745) = 0.1056P(W>745)=0.1056 and P(W<580)=0.25\text{P}(W < 580) = 0.25P(W<580)=0.25,
(i) find two equations in terms of μ \mu\,μ and σ\sigmaσ,
(ii) hence, showing your working, find the value of μ \mu\,μ and the value of σ\sigmaσ.
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.