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The director of manufacturing of a toy company is investigating vendors who supply handheld gyroscopes for inclusion into one of their most recent product lines. The director would like to estimate the diameter of gyroscope that are currently used in the toy line to determine if they still comply with the product specifications. The principal manufacturing vendor has specified that the gyros are supposed to have a population mean diameter of 7.30 inches and a standard deviation equal to .04 inches. A random sample of 25 selected from a shipment indicates a sample average of 7.31 inches. Set up a 95% confidence interval estimate of the true average diameter of the gyroscope in this shipment. Does the population of gyros need to have a diameter that is normally distributed here?

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