(5 points each) An adjustment to a metal stamping machine will change the length of a part but will not affect the standard deviation of the cut. The length of the parts is normally distributed with a standard deviation for all parts of 0.5 mm. A random sample of parts is taken after an adjustment of the machine. The following parts are measured in millimeters: 75.3, 76, 75, 77, 75.4, 76.3, 77, 74.9, 76.5, 75.8 a. What is the mean of the sample? What is the point estimate for u? b. Determine the 99.5% confidence interval for the population mean length for the part. c. Determine the 99.9% confidence interval for the population mean length for the part. d. Determine the minimum sample size needed for an estimate within 0.1 mm. Assume 99.5% confidence. e. Determine the minimum sample size needed for an estimate within 0.01 mm. Assume 99.9% confidence