At a physical therapy center, doctors work with patients to develop an exercise treatment plan to combat injuries. Assume that the time spent doing pool exercises per week has an unknown distribution with a mean of 4.5 hours and a standard deviation of 0.9 hours. A doctor believes most patients at the physical therapy center swim more per week. If the doctor randomly selects 32 physical therapy patients, what is the probability that the average time spent swimming per week is over 4.7 hours?