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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.