The operational flight time, DDD minutes, of a specialized surveillance drone on a single battery charge is modelled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ. Given that μ=45\mu = 45μ=45 and σ=2.5\sigma = 2.5σ=2.5, use standardisation to:
(i) show that P(D<41.5)=0.0808P(D < 41.5) = 0.0808P(D<41.5)=0.0808 to four decimal places. (ii) find the value of d0d_0d0 such that P(D<d0)=0.0150P(D < d_0) = 0.0150P(D<d0)=0.0150
A fleet manager randomly selects 5 drones from the production line.
Calculate the probability that every one of the 5 drones has a flight time exceeding 41.5 minutes.
A software update is applied to the drones such that the flight time, DDD minutes, now has a mean μ=48\mu = 48μ=48 and a new standard deviation σ\sigmaσ.
Given that P(D<d)=0.0548P(D < d) = 0.0548P(D<d)=0.0548 and P(D>1.5d−21)=0.0082P(D > 1.5d - 21) = 0.0082P(D>1.5d−21)=0.0082,
determine the value of ddd and the value of σ\sigmaσ.
