An elevator rail is assumed to meet specifications if its diameter is between 0.98 and 1.01 inches. Each year a company produces 100,000 elevator rails. For a cost of $100/ α^2 per year the company can rent a machine that produces elevator rails whose diameters have a standard deviation of α . the idea is that the company mist pay more for a smaller variance. Each such machines will produce rails having a mean diameter of one inch. Any rail that does not meet specifications must be reworked at a cost of $12. Assume the diameter of an elevator rail follows a normal distribution.

What standard deviation (within 0.001 inch) minimizes the annual cost of producuign elevator rails. You do not need to try standard deviations in excess of 0.02 inches. (Hint: Use a one-way data table; take starting trial value for SD as 0.005, and then use increments of .001 up to and including .01.)