The weights of bags of sugar, W W\,W grams, are normally distributed. It is known that P(W<490)=0.15P(W < 490) = 0.15P(W<490)=0.15 and P(W>515)=0.25P(W > 515) = 0.25P(W>515)=0.25.
Find the mean and standard deviation of the weights of the bags of sugar.
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.