If the dispense rate is approximately normal was their decision reasonable?

Question

A drink dispenser dispenses liquid with a mean of 500ml and a standard deviation of 20ml. The machine suffered a fall and afterwards was checked by a technician. The technician found the mean of the next 16 drinks was 485ml and determined no adjustment was necessary. If the dispense rate is approximately normal was their decision reasonable? (Their decision is unreasonable if the probability that the dispenser outputs more than 15ml (up or down) away from the mean is less than 5%)

Answer 1

The small sample of 16 suggests a t-test with 15 degrees of freedom for a 95% confidence interval (2-tailed). From tables, the t value is about 2.13. The pop SD needs to be reduced because of the sample size to 20/√16=20/4=5, and we need to find X where 2.13=(X-485)/5, so X-485=10.65ml. This I interpret to mean that for 95% confidence, if the dispenser outputs more than 10.65ml away from the mean then their decision is unreasonable. 15ml is greater than this, so their decision is unreasonable.