I was just wondering at how many weeks pregnancy does the typical woman find out the sex of the baby?

Depends on test. In the hands of an experienced technician using a sensitive ultrasound & with the cooperation of the baby, male parts can sometimes be detected at 10 wks. I wouldn't paint the nursery pink based on a negative reading at that point.A brief ultrasound done to verify placental location & gestational size may not be adequate to provide the information.
19 weeks. It is possible with a number of technologies to determine sex at an earlier time but typical is 18-20 weeks when a anatomy scan is routinely done for other indications.