Write SQL query to solve given problem: How many 2-year private nonprofit schools in "CT" whose graduation rate falls below the average for the state?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT COUNT(DISTINCT T1.chronname) FROM institution_details AS T1 INNER JOIN state_sector_grads AS T2 ON T2.state = T1.state WHERE T2.state_abbr = 'CT' AND T2.level = '2-year' AND T1.control = 'Private not-for-profit' AND T1.awards_per_value < T1.awards_per_natl_value