Are you looking for something like this?
Cereal dispensing machine problem
Suppose the standard deviation is not known but can be fixed at certain levels by adjusting the cereal dispensing machine. What is the largest std. dev. that will allow the actual value of cereal dispensed to fall within 1 ounce of the mean with prob of at least .95?
The mean is 11.67 oz. per box of cereal.
This involves Z-scores I'm pretty sure...