Is it normal for a 17 year old boy to go out with a 14 year old girl?

I would really say no because that is a huge age difference.

It is not abnormal because the age difference is so close, however as a 14 year olds maturity is likely to be different than a 17 year olds you should stick to being friends, any kind of sexual contact/play should be avoided. There are some legal issues involved here. Act responsibly !