Thanks for posting. It's actually more common these days for engineers to apply to business school than it used to be, though I understand your point in terms of not having a background in finance or consulting or similar. But keep in mind, in general business schools are open to a variety of backgrounds, and aim to create a 'micro-cosm' of the world within the b-school class. They do expect you to demonstrate quantitative and academic ability, and to be able to make a clear, rationale and compelling case for why business school, and how your past relates to your future goals, and how the MBA will connect both of those.
Congrats on an outstanding GMAT score, that goes a long way towards demonstrating that you can handle the academic rigor of the program, even with a below-average GPA (at least at top b-schools). As an engineer, you'll just want to ensure you stand out from OTHER engineers, and don't fall into a trap of just focusing on technical accomplishments.... if possible, aim to really showcase leadership, teamwork, communication skills, people management, influencing others, etc.
What I like about what you've shared as well is how you've started to connect your past experience with your future goals and explained how that makes sense, and how the MBA will help... encourage you to build upon that as it's an important step that some applicants struggle with.
If you put together strong essays (so important in a competitive environment), yes I think you could possibly have a shot even at top 10 programs, or you could at least choose one to apply to as a reach school. I would think you'd have good chances at Georgetown and Kenan-Flagler, with Darden a step up from there.
Keep us posted on questions and what you decide, wishing you the best!
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