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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.