A machine produces metal pieces that are cylindrical in shape. A sample of pieces is​ taken, and the diameters are found to be 0.94​, 0.96​, 1.02​, 1.04​, 1.05​, 0.98​, 0.97​, 0.94​, and...

A machine produces metal pieces that are cylindrical in shape. A sample of pieces is​ taken, and the diameters are found to be 0.94​, 0.96​, 1.02​, 1.04​, 1.05​, 0.98​, 0.97​, 0.94​, and 0.97 centimeters. Find a 99​% confidence interval for the mean diameter of pieces from this​ machine, assuming an approximately normal distribution.