I always guessed that the Caltech undergraduate cognitive ability threshold was roughly few per thousand (perhaps even 1 in 1000) in the general population -- that's what the test scores imply. Although the kids are smart there is still a broad distribution on campus in the ability to learn core subjects like the required two years of math and physics (keep in mind -- these are Caltech-level courses!).
Based on my experience I would guess that the threshold ability to understand (for example) quantum mechanics is pretty high. A good chunk of the Caltech class doesn't grasp QM despite taking a year of it as sophomores -- and these are hard working, self-selected kids, in addition to being very smart. In our U Oregon study of psychometric thresholds, we found that kids in the top 1% of math ability (say, SAT-M > 750) had only a 50% chance of graduating in the physics major with more A's than B's -- i.e., in-major GPA > 3.5. Note, thanks to grade inflation the in-major average GPA in physics, as in other majors at Oregon and at other public universities (vs even higher averages at private schools), is something like 3.2, so 3.5 is not a high threshold (about
In other words, asking someone to explain Schrodinger's equation and the two slit experiment to you is probably a better verification of high end cognitive ability than any standardized test. (I wrote verification because understanding of QM is a sufficient but not necessary indicator of brainpower... some very smart people never study QM ... too bad for them!)
Here's what Vernon Smith (Nobel Prize in econ; started as a physics major at Caltech but bailed into EE and then econ ;-) had to say:
The first thing to which one has to adapt is the fact that no matter how high people might sample in the right tail of the distribution for "intelligence," ... that sample is still normally distributed in performing on the materials in the Caltech curriculum. The second thing you learn, if you were reared with my naive background, is the incredible arrogance that develops in conjunction with the acquisition of what you ultimately come to realize is a really very, very small bit of knowledge compared with our vast human ignorance. ... the difference between Harvard and Caltech: "At Harvard they believe they are the best in the world; at Caltech they know they are the best in the world."