A machine fills bottles with water. The amount of water in each bottle, W W\,W ml, is normally distributed with mean 500 ml.
It is given that 30% of bottles contain more than 504 ml.
Find the value of k k\,k for which P(k<W<505)=0.45P(k < W < 505) = 0.45P(k<W<505)=0.45. Give your answer to 1 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.