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.
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.