The burst altitude of SkyBound meteorological balloons, HHH metres, is normally distributed with mean 32,000 metres and standard deviation 1,400 metres.
(i) Find P(H≠32000)P(H \neq 32000)P(H=32000).
(ii) Find P(30000<H<35000)P(30000 < H < 35000)P(30000<H<35000).
Determine the altitude exceeded by 70% of SkyBound balloons.
A competing brand, AeroVantage, has a burst altitude YYY metres modelled by a normal distribution with mean 28,000 metres and standard deviation σ\sigmaσ. Given that 18% of randomly selected AeroVantage balloons burst below 26,000 metres, find the value of σ\sigmaσ, correct to three significant figures.
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.