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.
