For your problem, you should start off by calculating the test statistic (in this case, mean of your estimator distribution which should be chi-square given sample is normally distributed) and also the variance of the distribution.
If you can do the above for this problem then understanding the rest of statistics will be a lot easier: all of statistics is about finding a distribution for something you are estimating and then using that to get the point estimate (usually the mean of the distribution but sometimes the median) and then using the distribution or the variance (sometimes you don't use the variance directly) to get your lower and upper bounds.
By showing your calculations for the mean of the chi-square of degree n and finding n then others can give you a critique on what you did right and/or wrong.
If you are using formulae, then you should have been given the formula for the point estimate of the variance and its distribution in terms of chi-square. Also, you will have to either use tables or a computer
program to calculate the lower and upper bounds of the confidence interval and if you need to use a computer to do it, I would recommend you use R.