Assuming that the number of questions answered is a gaussian random variable , you have to use the confidence interval for the Student distribution: you know that is distributed according to a Student distribution with degrees of freedom, where is the size of the sample, and and are the empirical mean and standard deviation.

By looking up in tables (or such as), you find a confidence interval for , i.e. a number such that or equivalently . This should be .

This gives you a confidence interval for : .

All that remains is to compute , from the data to deduce the bounds of this interval.