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.
228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.