The length of steel bolts produced by a machine is normally distributed with a mean of 50.0 mm and a standard deviation of 0.8 mm.
Find the probability of a bolt being longer than 51.5 mm.
The technician suspects that the mean length of the bolts has changed.
Write down a null and alternative hypothesis for a two-tailed test.
A sample of 16 bolts is measured and the mean length is found to be 50.5 mm.
Test at the 10% significance level whether there is evidence that the mean length has changed.
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.