The weight of beans in a tin produced by company A normally distributed with a mean of 415 g and a standard deviation of 3.4 g.
Find the probability that a randomly selected tin of beans has a weight of less than 409 g.
Write down the company's null and alternative hypothesis.
A sample of 20 tins is taken and the mean weight is found to be 413 g. Carry out a test at the 1% significance level to see if there is evidence that the machine is producing tins with a mean of less than 415 g.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.