You being a female is a tricky question. First of all, realize that generally speaking, you aren't competing with other applicants nationally. Most applicants are competing for the nomination from their rep/senator (MOC). Therefor, you're competing with people in your district/state. I say MOST applicants, because there are some other nominations other than your representative/senator; and if you're eligible for those, you'd be competing with other applicants who could be national.
Now, while the military academies don't have an actual "Affirmative Action" program in place for accepting candidates, they do understand URM. (Under-Represented-Minorities). They like to have an academy and a military that is representative of our society/country as a whole. So, while there are definitely less women in the academy than men; there's also a lot less applying. While your sex or race could play some part in the process, it's not a large part. And if anything, being a women could actually give you a slight edge. But realize, how the break down works. Here it is again for the Air Force Academy:
ROUGHLY 10,000 people apply to the academy (Prospects)
Roughly 6,500 of those will be considered worthy of consideration (Applicants)
Roughly 3,500 of those will be considered competitive (Candidate)
Roughly 1,700 of those will be offered an Appointment (Appointment offered)
Roughly 1,400 of those will accept the Appointment (Appointment accepted)
Now realize, that of those considered candidates (That 3,500 number can definitely be much higher if there's a lot of highly qualified applicants); these HAVE TO as a minimum have their entire application complete, CFA, DODMRB, and most importantly, a NOMINATION. Without this being accomplished, they can't even be considered to be offered the appointment.
The Army ALWAYS gives candidate status earlier than the Air Force. Matter of fact, it is not uncommon for West Point to give out LOA's in July. The final individual still has to have completed the same application and nomination, but the Army gives theirs out earlier in the hopes of getting people to lean more their way. (Sort of like colleges who offer Early-Acceptance in the Fall).
So, when it comes to competing, you are primarily competing with others in your district and state. Each person who nominates, is only allowed "X" amount of people in the academy at one time. So even though they can nominate 10 individuals each year, it's possible that they aren't ALLOWED to have but 1 or even 0 out of that list in this particular year. But if your application is a kick butt application, walks on water, then the academy will work to find you another nomination. And if you can get the #1 slot of the nomination on your representative's list, then as long as they have a slot available, and you're qualified according to the academy, then you are also in. Hope this sort of explains (In an overly simplified way) how the process works. best of luck. Mike....