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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.