Question 2: (10 marks) A tyre manufacturing company recently modified its manufacturing technique and wants to know if this has improved the average running life of their tyres. 75 tyres are randomly selected from a large production line and tested; their average running life is found to be 750 kilometres more than their previous average. a. What is the population of interest? What is the sample? What is point estimate of the average improvement in running life of the tyres? (3 marks) b. C. Assuming the sample is drawn from a normal population, calculate the 95% confidence interval estimate of the average improvement in running life of the tyres (given that sample standard deviation s = 300 hours). (2.5 marks) Assuming the sample is drawn from a normal population with a population standard deviation of 300. Calculate the 95% confidence interval estimate of the average improvement in running life of the tyres. (2.5 marks) d. Explain why the interval estimate in Part-c is narrower than that in Part-b. (2 marks) Note: You are required to show your workings and calculations for this question.