Confidence Interval of a bounded variable [duplicate]

Given a random variable $$X$$ which can take values on $$[0,1]$$. I am interested in calculating the confidence values for the mean estimator. We know that the mean is normally distributed and can calculate the regular confidence value, but they lie outside of $$[0,1]$$. How do you deal with this do you intersect the confidence value with the range $$[0,1]$$?