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.
228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.