Several decades ago, Christopher Boorse formulated an influential statistical theory of normative biological functions but it has often been claimed that his theory suffers from insuperable problems such as an inability to handle cases of epidemic and universal diseases. This paper develops a new statistical theory of normative functions that is capable of dealing with the notorious problem of epidemic and universal diseases. The theory is also more detailed than its predecessors and offers other important advantages over them. It is argued here that statistical theories of biological functions should not be so quickly dismissed