A soft-drink factory fills bottles of soda by setting a timer on a filling machine. It has generally been observed that the distribution of the number of ounces the machine puts into a bottle is normal, with standard deviation 0.05 ounce. The company wants 99.9% of all its bottles to have at least 16 ounces of soda.
To what value should the mean amount put in each bottle be set? (Of course, the company does not want to fill any more than is necessary.)