The length of the bus journey from Leeds to London is normally distributed with a mean of 212 minutes and a standard deviation of 6 minutes.
Find the probability of a bus taking longer than 224 minutes.
The bus company suspect that the mean bus time has changed.
The null and alternative hypotheses are
H0:μ=212andH1:μ≠212 H_0:\mu=212 \quad \text{and} \quad H_1:\mu\neq212 H0:μ=212andH1:μ=212Write down whether the test should be one-tailed or two-tailed.
They take a sample of 9 bus journeys and find a mean time of 218 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.