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? Drag and move the blue dot to select the appropriate probability graph area from the four options on the left. (Note - there are four graphs available to choose from. Only select between less than, greater than, and area between graphs.); Use the Central Limit Theorem to find μx¯ and σx¯; Calculate the z-score for x¯=4.7 and move the slider along the x-axis to the appropriate z-score; The purple area under the curve represents the probability of the event occurring. Interpret the purple area under the curve. Round μx⎯⎯⎯ to one decimal, σx⎯⎯⎯ to three decimals, and P(x⎯⎯⎯>4.7) to four decimal places.