The volumes of specialized propellant canisters, V V\,V ml, are modeled by a normal distribution with mean 450 ml and standard deviation 12 ml.
Determine the probability that a canister chosen at random from the production line contains more than 432 ml.
A specific high-pressure canister, 'Titan-X', is ranked at the 85th85\text{th}85th percentile for volume within this distribution.
Calculate the volume of propellant in the 'Titan-X' canister.
A different propellant, 'Solvent-B', has canisters whose volumes, W W\,W ml, are normally distributed with a standard deviation of 15 ml.
Given that 98% of 'Solvent-B' canisters have a volume greater than the mean volume of the V V\,V distribution,
find the mean volume of a 'Solvent-B' canister, giving your answer to one decimal place.
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.