The volume of orange juice in a carton produced by a bottling machine is normally distributed with a mean of 252 ml and a standard deviation of 3.5 ml.
Find the probability that a randomly selected carton of orange juice contains less than 245 ml.
Write down the null and alternative hypotheses to test if the mean volume is lower than 252 ml.
A sample of 30 cartons is taken and the mean volume is found to be 251 ml. Carry out a test at the 5% significance level to see if there is evidence that the machine is producing cartons with a mean of less than 252 ml.
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.