17. (5) A company produces bottled water. The volume of water the bottling machine puts into each bottle is distributed normally with a known standard deviation of 10 ml. Each bottle needs to be filled to 500 ml, but small variations to either side are acceptable. In a random sample of 5 bottles, the following volumes are observed: 502, 529, 454, 510, 545 (a) Does it appear that the machine is working as expected? Use 0.10 significance. (3) (b) Give the 90 % confidence interval for the mean fill amount. Explain how it matches your answer to (a). (2)