Consider an Engine Parts Supplier and Suppose the Supplier Has

Consider an engine parts supplier and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s² = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. Using the upper end of the 95 percent confidence interval for σ and assuming that
μ = 2.5, determine whether 99.73 percent of the outside diameters produced by the new machine are within the specification limits.