The school canteen sells coffee in cups claiming to contain 250 ml. It is known that the amount of coffee in a cup is normally distributed with standard deviation 6 ml. Adam believes that on average the cups contain less coffee than claimed.
Adam decides to collect a large sample. He finds the average to be 248 ml again, but this time this is sufficient evidence to conclude at the 1% significance level that the average amount of coffee in a cup is less than 250 ml. What is the minimum sample size he must have used?
I do not know where to start, as I have always calculated the normal distribution probabilities (cdf - cumulative) using a GDC...How can I reverse the process to find $n$, the sample size?