1) calculate standard error of the sample mean SEM = sigma/sqrt(n) = 9.011
2) calculate z-score. Your value of 1.35 for 82% looks correct.
3) now multiply the values obtained in steps (1) and (2) above.
This is the limiting value.
4) Add (subtract) the value obtained in step (3) to the mean value 258.5 to get upper (lower) confidence limits.
where a numerical example is worked out and all the 4 steps given above are
explained in detail.
Hope this helps