Let X be the amount of soda released by a soft-drink dispensing machine into a 6-ounce cup. Assume that X is normally distributed with σ = .25 ounces and that the average "fill" can be set by the vendor.
(a) At what quantity should the average "fill" be set so that no more than .5% of the releases overflow the cup?
(b) Using the average "fill" found in part (a), determine the minimal amount that will be dispensed in 99% of the cases.