Does it mean I am admitted if the College emailed me to confirm my major?

I received a letter from NYU several days ago. The admission officer noticed that I write about business in my essay but choose economics and math as my major and would like me to make sure if it was a mistake. I choose this major because I believe it would lay fundamental to my future business study and career. I wonder if this email means that my application has been reviewed and I have great chance to get in?

No I would not assume this means you are admitted nor would I infer anything about your chances to be admitted. I would guess that it means your admissions officer wants to be sure you have applied to the school you actually want to attend (ex. liberal arts v Stern). I would reply with a short email/note – with the brief explanation you have above, a confirmation of your choice of school, a thank you for his/her time and interest in your application, and you can also affirm your interest in NYU. Just a few well written sentences should do the trick.