Problem 1: A machine is producing metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 cm. Find a 99% confidence interval of the true mean diameter of pieces from this machine, assuming an approximate normal distribution.