The flight duration of a specialized cargo drone, TTT minutes, is modelled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ. Given that μ=110\mu = 110μ=110 and σ=12\sigma = 12σ=12, use standardisation to:
(i) show that P(T<95)=0.1056P(T < 95) = 0.1056P(T<95)=0.1056 (ii) calculate the value of t0t_0t0 such that P(T<t0)=0.0228P(T < t_0) = 0.0228P(T<t0)=0.0228
An operator randomly monitors 3 independent drone flights.
Calculate the probability that each of the 3 flights lasts longer than 95 minutes.
The drone's battery system is upgraded such that the new flight duration, XXX minutes, has mean μ=115\mu = 115μ=115 and standard deviation σ=s\sigma = sσ=s.
Given that P(X<x)=0.1587P(X < x) = 0.1587P(X<x)=0.1587 and P(X>1.4x−29)=0.0228P(X > 1.4x - 29) = 0.0228P(X>1.4x−29)=0.0228,
find the value of xxx and the value of sss.
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.