Is gender construction culturally or biologically based?

Gender and sex have long been recognized as being two distinct characteristics. Sex refers to the sex organs with which a person is born, as well as their chromosomes (XX=female, XY=male).
Gender refers to characteristics that distinguish masculinity and femininity, and an individual's gender identity may or may not match the sex organs he or she possesses. That is, males may exhibit characteristics commonly associated with females, and vice versa. 
So the question is, does a person exhibit male or female characteristics because they have a certain biological makeup, or does a person exhibit male or female characteristics because he or she is conforming to the expectations of their culture? 
It is largely agreed that while sex is biological, gender is a function of culture and/or society. 
Arguments for gender being a function of culture: 
-Men and women adhere to different norms in different cultures. If gender were entirely biological, the same behaviors would be observed in men and women throughout every modern and ancient culture. 
-Within any culture, there are individuals who do not conform to the typical characteristics ascribed to their sex. 
-Some individuals are intersex (meaning they posses both male and female sex characteristics) and yet still have a gender identity. 
-Some cultures acknowledge more than two genders. If gender were biologically determined, the gender distinctions would be the same in all human societies. 
In summary, gender construction is determined by the cultural expectations for each biological sex. This is why there are two separate definitions for each concept, even though for the majority of individuals, their sex and gender and the same.