[disgruntledphd2]

That is correct.

So the SATs are (almost certainly) 3-pl (actually 2) IRT models. Essentially, it's a multivariate generalised linear mixed model to estimate both question difficulty and participant ability.

Normally, they'll estimate the abilities on the logistic scale, and use the percentile to back transform to a standard normal.

Most people don't cluster at the top because they are a good proxy for g, which is an imaginary statistical construct that we use to explain differences in school outcomes.

So I had a long digression here about the usefulness of penalties for guessing, but it turns out the SATs don't do that anymore, so wth?

(ETS invented IRT, that's why I'm pretty sure).