scores on a certain test are normally distributed with a varience of 82. A researcher wishes to estimate the mean score achieved by all adults on the test. Find the sample size needed to assure a 98% confidence that the sample mean will not differ from the population mean by more than 2 units.

I am confused, i am not sure if the varience is used to find the population standard deviation or the sample standard deviation???

I went with population sd here is what i have, am i on the right or do i need to use the tdistribution??

varience 82 .......population sd= 9.0

z=2.33 e=2 popsd=9.0

n=305.38 rounded to 306