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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.