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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.