A tech logistics company monitors the flight duration of its delivery drones. The flight duration during the summer, S S\,S minutes, is modelled by a normal distribution S∼N(320,242)S \sim \text{N}(320, 24^2)S∼N(320,242).
Using standardisation and showing your working, determine the probability that, for a drone flight selected at random in the summer,
(i) the duration exceeds 284 minutes,
(ii) the duration is 320 minutes, correct to the nearest 16 minutes.
The flight duration during the winter, W W\,W minutes, is modelled by W∼N(μ,σ2)W \sim \text{N}(\mu, \sigma^2)W∼N(μ,σ2).
Given that P(W>280)=0.0901\text{P}(W > 280) = 0.0901P(W>280)=0.0901 and P(W<220)=0.2810\text{P}(W < 220) = 0.2810P(W<220)=0.2810,
(i) find two linear equations in terms of μ \mu\,μ and σ\sigmaσ,
(ii) hence, showing your working, calculate 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.
