For this question from a large amount of data I have calculated that the mean is 44.22, the sample size is 100 and the standard deviation is 22.0773.

From this I am asked to , make the 98% confidence intervals for the (1) true mean µ of the module mark (2) true variance of the module mark

And for each: (a) Determine what quantity to look at, and which distribution table to use, justifying your choice. (b) Determine the number of degrees of freedom, justifying your answer. (c) Calculate the actual intervals.

So far for 1, I have used the z table to look for 99% as I need 1% to the right of 2.33 and 1% to the left of −2.33, so 98% is between $\pm 2.33$. Giving me

$$\overline{x}\pm 2.33\frac{\sigma}{\sqrt{n}}$$

Which provides me with a 39.08 to 49.36 confidence interval, is this correct? And how would I determine degrees of freedom and go about answering part 2?