No, it is not normal. It is likely she displays hyperactivity and, when such a condition is interfering with normal development, it invites treatment (or, at the very least, evaluation). In addition, you might ask the pediatrician for a referral to a pediatric sleep disorder clinic. My sense is that the hyperactivity syndrome is the cause of the abnormal sleep pattern, but the sleep disorder clinic could figure this out.
Thank you for your response. I had been thinking for a while that she might have something like that cause I see her at dance class with girls her own age or even younger and she does not act like a typical 3 year old. As I said she excessively talks all day and when we are home she runs back and forth from her room to the living room. She is an intelligent girl but it is so hard to discipline her. Just the other day she spit in my face cause I put her in time out. I was told by the nurse at my doctor's pediatrician to try and change our night time routine a little and see if that helped with her sleeping late if not they told me to wake her up earlier and tell the daycare to only let her sleep for one hour. She is also overly picky too. Like she has a Dora blanket and if I put Dora facing the bottom of the bed she freaks out and starts yelling at me saying I want Dora so I put Dora facing up and then once I do that She'll say No I Want boots which had already been facing her to begin with. Is that typical in a 3 year old? Sometimes I have to even fight with her to take a bath cause she wont want to and she screams and cries. I was wondering if eating a lot of candy while pregnant could have caused her to be such a hyper child? Cause when she was in the womb she also never stopped moving. She was continuously moving around.