I can't remember how to figure out this type of problem. I swear I figured this out once before, but now I am clueless..

Let's say there's a certain achievement test and you know that 5th graders in general score a mean of 200 on the test. The known standard deviation of the population is 48 on this test.

You hypothesize that giving a group of 5th graders special instructions before the test (to choose the first answer that comes to mind) will cause them to score higher. The predicted mean is 208 for this group.

What I want to find now is how many 5th graders I would need in my sample size for the power of the study to be 80%.

What I have figured so far is that z-score I will need to get on my distribution of means for population 1 (based on the research hypothesis) is -.84.

The standard deviation on that distribution of means will be 48/ sqrt(N).

N being the number of kids in my sample. The mean will be 208.

I know that z = (x-m)sd but I am stuck on how to solve from here.

I would appreciate any help. Thanks!