Tell the number of 4-year public schools in UT whose graduation rate exceeds the average for the state.
4-year refers to level = '4-year'; public refers to control = 'Public'; UT refers to state_abbr = 'UT'; graduation rate exceeds the average for the state refers to awards_per_value > awards_per_state_value;
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 = 'UT' AND T1.level = '4-year' AND T1.control = 'Public' AND T1.awards_per_value > T1.awards_per_state_value