The length of the bus journey from Leeds to London is normally distributed with a mean of 220 minutes and a standard deviation of 8 minutes.
Show that the probability of a bus taking longer than 235 minutes is 0.0304.
Write down a null and alternative hypothesis for a two-tailed test.
They take a random sample of 10 bus journeys. The standard deviation remains 8 minutes and they find a mean time of 230 minutes. Test at the 1% significance level whether there is evidence that the mean time 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.