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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 439 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
