A machine produces metal pieces that are cylindrical in shape. A sample of these pieces is taken and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 1.01, 1.03, 0.99, 1.00, 1.00, 0.99, 0.98, 1.01, 1.02, 0.99 centimeters. Use these data to calculate three interval types and draw interpretations that illustrate the distinction between them in the context of the system. For all computations, assume an approximately normal distribution. The sample mean and standard deviation for the given data are 1.0056 and 0.0246. (a) Compute a 99% confidence interval on the mean diameter. (b) Compute a 99% prediction interval on the next diameter to be measured. (c) Compute a 99% tolerance interval for coverage of the central 95% of the distribution of diameters.