A filling process at your plant injects a specialty dielectric filling into an exterior wall for the product. To meet standards, the process must inject 10 cubic centimeters of dielectric, or the wall must be reprocessed at a cost of $20. The quantity injected is normally distributed with a mean of 10 cubic centimeters and a standard deviation of 0.4 cubic centimeters. A cubic centimeter of this dielectric costs $10. A correctly constructed wall is $230 of the overall build price.
a. What is the probability that the wall will be underfilled?
b. The manager wants to adjust the mean to reduce the reject rate. Compute the probability of underfilling for several values of the mean fill. How much extra per wall does it cost to ensure a 99% acceptance rate?