The scores on a standardised aptitude test are modelled by a normal distribution with mean 50 and standard deviation 8.
Using this model, find the probability that a randomly chosen candidate scores more than 65. Give your answer to 3 significant figures.
A researcher claims that the mean score of candidates from a particular region is higher than 50. A random sample of 64 candidates from this region has a mean score of 52.
Stating your hypotheses clearly, test the researcher's claim at the 5% significance level. You may assume that the standard deviation is 8 for this region.
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.