The mass of coffee in a jar, in grams, is modelled by a normal distribution with mean 200 g and standard deviation 4.2 g.
Find the probability that the mass of coffee in a randomly chosen jar is more than 205 g. Give your answer to 3 significant figures.
Find the probability that the mass of coffee in a randomly chosen jar is between 195 g and 205 g. Give your answer to 3 significant figures.
The manufacturer states that no jar contains a negative mass of coffee. Explain why this does not make the normal model unreasonable here.
A histogram of the masses is approximately symmetric and bell-shaped, with its highest bars near 200 g and changes of curvature near 195.8 g and 204.2 g. Explain how these features are consistent with the stated normal model.
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.