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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.