there's a distinction between random variables that are assumed to actually be normal and RVs that we conceptually apply the clt to and then treat as normal. i

there's a distinction between random variables that are assumed to actually be normal and RVs that we conceptually apply the clt to and then treat as normal. in the case of test scores it could be either. for an individual test it's possible the distribution is roughly normal actually. but if you, for example, look at subsets of all SAT scores and take their means (the mean of the subset) then those averages will be Bell shaped because of the clt. Just to directly answer your question: the iid random variable is the test score or the iq.