Question: In order for a cylindrical engine part to give an engine long life, the outside diameter of the part must be between the specification limits

In order for a cylindrical engine part to give an engine long life, the outside diameter of the part must be between the specification limits of 2.95 inches and 3.05 inches. Assuming normality, determine whether 99.73 percent of the outside diameters produced by the current machine are within the specification limits.
Consider an engine parts supplier and suppose the supplier has determined that the mean and the variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 3 inches and .0005. To reduce this variance, a new machine is designed, and a random sample of n = 25 outside diameters produced by this new machine has a mean of 3 inches, a variance of .00014, and a bell-shaped and symmetrical histogram.

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