The time taken by a bus to travel from Leeds to London, in minutes, is normally distributed with mean 220 minutes and standard deviation 8 minutes.
Find the probability that a randomly chosen journey takes longer than 235 minutes. Give your answer to 3 significant figures.
The bus company suspects that the mean journey time has changed. A random sample of 10 journeys is taken, and the mean time for the sample is 230 minutes.
Stating your hypotheses clearly, carry out a two-tailed test at the 1% significance level to investigate the company's suspicion. You may assume that the standard deviation is still 8 minutes.
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.