The mass of beans in a tin filled by a machine, in grams, is normally distributed with mean 415 g and standard deviation 3.4 g.
Find the probability that a randomly chosen tin contains less than 409 g of beans. Give your answer to 3 significant figures.
The company suspects that the machine is now filling tins to a mean mass of less than 415 g. A random sample of 20 tins is taken, and the mean mass of beans in the sample is 413 g.
Stating your hypotheses clearly, carry out a test at the 1% significance level to investigate the company's suspicion. You may assume that the standard deviation is still 3.4 g.
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.