As a young citizen member of in the modern society, I have dreams and goals that motivate me. It is essential to learn everything that I can so I can in order to achieve my goals one day and be able to serve the society and my country.
Throughout the years, I was in school, I workeding hard towards that my goal to be of becoming a nurse.
I want to be able to help people and make them smile. ---- strong idea, I also suggest(only a suggestion);
"I want to be someone who would make people smile"
Rutgers would be able to help me pursue my dream, and give by providing me with a high level of quality education. ----- The part in red does not convey that you are sure of Rutger's capability. In my view, it is better that you show them that you are convinced about their capability;
Rutgers would certainly help me pursue my dream, by providing me with a quality education.
Not only that, but also the vibrant community of people will open my eyes to things I never thought about. ----- here the reader gets the feeling that you tend to use the same words as they are in the prompt. I feel it is better if you can paraphrase it;
Also, the Rutgers community, being so diverse and vibrant, would certainly help me broaden my perspectives.