A textile company produces spools of yarn. The length of yarn on each spool, Y Y\,Y m, is normally distributed with mean 150 m. Given that 25% of spools contain more than 154 m.
Find the value of k k\,k such that P(k<Y<155)=0.60P(k < Y < 155) = 0.60P(k<Y<155)=0.60.
The machinery is serviced so that the standard deviation of the length of yarn is now 5 m. Following the service, the supervisor believes that the mean length of yarn is less than 150 m. A random sample of 100 spools is checked and found to have a mean length of 149.2 m. Test the supervisor's belief at the 5% significance level. You should state your hypotheses clearly.
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.