A machine produces metal pieces that are cylindrical in shape. A sample of these pieces is taken and the diameters are f

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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. 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 ¯x = 1.0056 and s = 0.0246. (a)
Find a 99% confidence interval on the mean diameter. (b) Compute a
99% prediction interval on a measured diameter of a single metal
piece taken from the machine. (c) Find the 99% tolerance limits
that will contain 95% of the metal pieces produced by this
machine.
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