The National Sleep Foundation reported that teenagers need $9\frac{1}{4}$ hours of sleep every night to perform at their best during the day, and that it isn't natural for teenagers to be able to fall asleep before 11:00 at night. My alarm goes off at 6:20 a. m. on weekdays. Even if I fell asleep at exactly 11:00 on the school nights, how far under the $9\frac{1}{4}$ quota would I be? Give your answer in hours as a mixed number. (Assume that I am a teenager.)