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, 0.99, 1.01, and 1.03
centimeters. For all computations, assume an approximately normal
distribution. (a) Compute a 95% confidence interval on the mean
diameter. (10 points)(b) Compute a 90% prediction interval on the
next diameter to be measured. (10 points)(c) Compute a 99%
tolerance bounds for coverage of the central 95%of the distribution
of diameters