Have been stuck on this question for weeks now, and I really need help with the solution.
The volume of a soft drink in a 1-litre bottle is normally distributed. The filling machine needs to be calibrated so that no more than 2% of bottles are more than 2mL under volume. Standard deviation = 2.5mL. What should the target volume be (mean) ?
SPOILER OF ANSWER: Answer = 1003mL
The problem is requesting that
$$\mathbb{P}[X<998]\leq 0.02$$
$$\mathbb{P}[Z<\frac{998-\mu}{2.5}]\leq 0.02$$
reading the quantile on the Standard Gaussian Table
$$\frac{998-\mu}{2.5}\leq -2.0537$$
$$\mu\geq 1003.1344$$