Are cows right-handed or left-handed?

When my mom started school she had a tendency to be left handed. Every time the teacher saw a kid writing with their left hand, they got rapped severely on the knuckles. The children were obliged to use their right hand. Many of these kids who were forced to change were almost ambidextrous throughout their lives.
Anyone who ever brought the milk cows in for milking and tried to make a cow stand on the side of the stall, (most old cow barns had double stalls where two cows stood, one on the right and one on the left) tried to force a cow to go to the right side of the milking parlour when she preferred the left side, or got kicked by a cow who was standing on the wrong side when they tried to milk her; understands that even cows prefer one side or the other.