Chemistry teacher gave us this statistics problem?

Question

Chemistry teacher gave us this statistics problem?

A bottling company wants to make as much money as possible but they have to follow rules by the government. The regulation is that no more than 2.5% of the bottles may contain less than the stated volume in the bottle. If the bottles that are being filled are stated to contain 100 mL, what is the minimum volume you should use for filling if the uncertainty in the bottle wall thickness accounts for + or - 1.2 mL and the uncertainty in the fill level is + or - 1.6 mL.

(The teacher gave us a hint: assume an infinite number of samples where the CI is X + or - st and t = 1.96 for 95% confidence and 2.58 for 99% confidence)

Answer 1

100.3 ml. your uncertainty is 2.8 ml, and your limit is 2.5ml. this will guarantee at least 97.5ml, which is within limits.