The mass of flour in a bag, W W\,W grams, is normally distributed. It is known that 5% of the bags weigh less than 495 g and 12% of the bags weigh more than 510 g.
Calculate the mean, μ\muμ, and the standard deviation, σ\sigmaσ, of the masses of these bags.
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.