The FDA does not allow meat to be sold with traces of antibiotics above strictly safe limits. The U.S. Food Safety and Inspection Service (FSIS) performs randomly scheduled testing of meat nationwide. According to FDA and FSIS regulations, livestock antibiotic use requires specific withdrawal times, or a set number of days that must pass between the last antibiotic treatment and the animal entering the food supply. This ensures the drugs have sufficiently cleared an animal’s system and the meat you purchase in stores is safe for you and your family to eat.
To get more of your questions answered, check out this brochure from American Meat Institute.