2. (2+4+4=10 points ) A machine can be adjusted so that under control, the mean amount of sugar filled in a bag is 5 pounds. To check if the machine is under control, a few bags were picked at random and their weights (in pounds) were found to be as follows: (a)Find the sample mean and the sample SD (use statistical functions of your calculator) (b) Find a 90% confidence interval for the true mean weight of a bag. Assume that the weights of sugar bags are normally distributed. Show your work. (c) Is there strong evidence to suggest that the machine is out of control? Test at 10% level. Show all work. (d) Could you have solved part (c) from part (b)? Explain