The battery life, in hours, for a fully charged wireless keyboard is normally distributed with mean 50 hours and standard deviation 6 hours. Hannah has a fully charged wireless keyboard.
Find the probability that the keyboard lasts longer than 45 hours.
Hannah uses her keyboard for 45 hours. Find the probability that Hannah's keyboard lasts for another 10 hours.
Hannah believes that the mean battery life of the wireless keyboards are longer than 50 hours. She took a random sample of 20 of these keyboards and found that their mean lifetime was 51.1 hours. Stating your hypotheses clearly and using a 5% level of significance, test Hannah's belief.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.