(a) A machine is set up such that the average content of juice per bottle equals . A sample of 100 bottles yields an average content of 270ml. Assume that the population standard deviation 45ml. Find (i) an estimate of the population mean and population variance; (ii) the standard error of the mean; (2 marks) (2 marks) (2 marks) (iv) the confidence interval for the confidence level 95%. (2 marks) (iii) the sampling distribution of the sample mean.