Can someone give you some examples of normative crime?

No. But here is a good definition of it:

" An abnormal behavior that goes against the existing norms and cultural standards.

The norms and cultural standards actually define how humans should conduct themselves."

Legally a crime is defined as an act which is forbidden by statute and thus is punishable by law. Therefore, crime can be taken as a specific act of deviance which breaks the formal rules or laws in a society.

Thus, a crime is something that is unacceptable to the society as well as being forbidden by the law.

Anything that is allowable by law, even though unacceptable to the society, is not a crime.