Bonus question: What if we change our constraints to only account for 3-sigma people? Does our conclusion change?
This speaks to their lack of confidence more than their capability. Perhaps that is one of the advantages a good school, a good peer group, or a good network can confer: the confidence to aim higher.
People don't think they're good enough... which may be true, but no one can truly know until they try. Self-limiting thinking is particularly prevalent in rust-belt cities and regions where knowledge or achievement is not prized, so people in knowledge-intensive fields have no models to emulate.
And sometimes when they try (it's not unusual for graduates of lower ranked universities to send out 300+ resumes only to get single digit responses), they get demoralized when they don't succeed on their first few tries, when in fact there's more than one path in life -- if one doesn't have natural advantages, one might have to embrace the more circuitous path(s). This can mean joining a startup, going to a better grad school than one's undergrad, moving to a better city to upgrade one's peer groups (this is more important than most people think [1]), etc.
Life can surprise you if you keep trying and pivoting (ugh cliche, but there it is). There's an element of randomness and stochasticity in a free market, and I've seen enough counterexamples to distrust a static conception of how things "should be". (except for some stodgy areas like investment banking that only hire from certain schools; but even then there are backdoors)
* You're a new graduate, and the hardest hurdle you have to overcome is to get in the door. If you manage to do that and are able to prove yourself, your undergrad degree will become less and less and important. If you google Fortune 500 company CEOs, especially in non-tech companies, (you can do this exercise for yourself) you will learn that many of them went to non-elite schools for undergrad. For all its elite colleges, America is not really an academic-technocratic society (unlike countries like Germany where most CEOs have Ph.D.s). There are elements of William James' pragmatic philosophy that still influence the thinking in this country -- getting results is more important than academic knowledge.
I can say that CSE was very selective when I was there, and getting into upper division was even harder. But overall I don't think acceptance rate is a very useful statistic because program size affects it so much.
[1] http://news.minnesota.publicradio.org/features/2005/06/10_ap...
