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.
Practise Edexcel A Level Maths Hypothesis Testing with the Normal Distribution with exam-style questions for A Level Maths. 132 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
