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.
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.