4.28 Durtco Incorporated designs and manufactures gears for heavy-duty construction equipment. One such gear, 9973, has the following specifications:

(a) Mean diameter 3.0 in.

(b) Standard deviation 0.001 in.

(c) Output normally distributed The production control manager has selected a random sample of 500 gears from the inventory and measured the diameter of each. Nothing more has been done to the data. How would you determine statistically whether gear 9973 meets the specifications?

Be brief but specific about which statistical procedure to use and why and outline the steps in the procedure.