An electronics firm manufactures high-performance drones. The continuous flight time of a 'SkyMaster' drone, T T\,T minutes, is modeled by a normal distribution with a mean of 42 minutes and a standard deviation of 4.5 minutes.
(i) Find P(T<35.5)P(T < 35.5)P(T<35.5).
(a) (ii) Find P(T>50)P(T > 50)P(T>50).
(a) (iii) To achieve an 'Endurance Rating', a drone must fly for a duration between 38 and 48 minutes. Determine the proportion of 'SkyMaster' drones that achieve this rating.
The firm also produces a 'Nano' model. The flight time of the 'Nano' model is normally distributed with mean μ \mu\,μ and standard deviation σ\sigmaσ.
Testing reveals that 10% of these drones have a flight time of less than 25 minutes, and 20% of these drones have a flight time greater than 35 minutes.
Find the value of μ \mu\,μ and the value of σ \sigma\,σ for the 'Nano' drones.
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.