Continuing the previous problem, suppose that SteelCo can pay money to reduce the standard deviation of the process. It costs e^100D dollars to reduce the standard deviation from 0.025 to 0.025 — d. (This reflects the fact that small reductions are fairly cheap, but large reductions are quite expensive.) If the company wants to make sure that at least 99% of all rods meet specifications, how much will it have to spend? (Remember that you evaluate e* in Excel with the EXP function.)

Data from previous problem

The SteelCo company manufactures steel rods. The specification limits on the lengths of these rods are from 95.6 inches to 95.7 inches. The process that produces these rods currently yields lengths that are normally distributed with mean 95.66 inches and standard deviation 0.025 inch.