Chance Me + best engineering schools?

Hi, I was looking for people rate my chances for admissions at top engineering colleges. I plan to major in mechanical engineering and will be graduating next spring.

Stats: 4.0 GPA, 36 ACT - without much test prep

Upon graduation I will have 3 semester of full-time classes at a local college with a (hopefully) 4.0 GPA still, along with advanced math (Calculus 2) and science courses.

EC’s: 3 yrs cross country, 4 golf, 4 in speech, 4 in robotics
-Moderate success in speech, but was unable to compete at state due to scheduling. I will also be senior captain this year.

Volunteering: Food shelf, 50 hrs/yr

My main concern is that besides great test scores and great grades in actual college classes, I dont have much for outstanding achievements that ivies look for. I come from a very small town (3k) that has very little to offer for academics and opportunities and I havent been able to do things like joining organizations, science research or internships. Where i live, high school teachers/counselors are more concerned with getting kids into college at all than getting anyone into top schools.

Anyway, I’d like some opinions on my admissions chances, taking into account my excellent profile (and my essays are quite good) despite a lack of any amazing achievements

Thanks,
High school senior

Do you have any past leadership in any of your clubs? How much commitment have you put in each? Also, try to provide a list of colleges you plan on applying for.

You got perfect score and GPA. I don’t the reason why you are asking for chances.
Make up your mind if you are thinking of Ivies or best engineering schools. There are not many options under these categories. Obviously, Ivies would have a lot of applicant like you and their admission rates are low, but you do have better chances than average applicants at those schools.

As far as past leadership, I don’t have anything official. Most sports at my school require captains to be seniors but II have unofficially been a leader in speech and robotics already.

More specific college list: Stanford, MIT, Carnegie Mellon, Cornell, Princeton
-Cornell and Carnegie Mellon are easier to get into but much more expensive for my family so I’m unsure about those
-These are just my reach/target schools, I’m also applying to my state school (decent engineering program but huge school) and one other that is nearby

I know I don’t have any schools that are in the middle of my choices but my thinking was that I only want to move out-of-state if I get in somewhere really good