An ecologist tracks the daily migration distance of a species of Arctic tern during its seasonal journeys. During the northward spring migration, the daily distance covered, D D\,D km, can be modelled by a normal distribution D∼N(450,402)D \sim \text{N}(450, 40^2)D∼N(450,402).
Using standardisation and showing your working, find the probability that, on a randomly selected day in spring,
(i) the distance covered is more than 394 km,
(ii) the distance covered is 450 km, correct to the nearest 60 km.
During the southward winter migration, the daily distance W W\,W km is modelled by a normal distribution W∼N(μ,σ2)W \sim \text{N}(\mu, \sigma^2)W∼N(μ,σ2).
Given that P(W>410)=0.0668\text{P}(W > 410) = 0.0668P(W>410)=0.0668 and P(W<330)=0.1587\text{P}(W < 330) = 0.1587P(W<330)=0.1587,
(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 Finding the mean and standard deviation with exam-style questions for A Level Maths. 48 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.
