you probablycan kill a truckload of zebra with a 22 shooting them all behind the ear, but the zebra is one tough customer. Remember 2 things in africa when using a light caliber. 1st you are going to pay for the animal if you hit him and he gets away. 2nd you will loose hunting time tracking wounded game.
For my part I would not recommended anything less than a 300 mag for zebra, and preferably something bigger.