Write SQL query to solve given problem: On average how many caffeinated root beers are sold a day?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT CAST(COUNT(T2.RootBeerID) AS REAL) / COUNT(DISTINCT T2.PurchaseDate) FROM rootbeerbrand AS T1 INNER JOIN rootbeer AS T2 ON T1.BrandID = T2.BrandID INNER JOIN `transaction` AS T3 ON T2.RootBeerID = T3.RootBeerID WHERE T1.Caffeinated = 'TRUE'