At a physicaltherapy 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 of4.5

hours and a standard deviation of0.9

hours. A doctor believes most patients at the physical therapy center swim more perweek.

If the doctor randomly selects32

physical therapy patients, what is the probability that the average time spent swimming per week is over4.7

hours?

1. Drag and movethe 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 areabetween graphs.);
2. Use the Central Limit Theorem to findxandx;
3. Calculate thez-score forx=4.7 and move the slider along thex-axisto the appropriatez-score;
4. The purple area under the curverepresents the probability of the event occurring.Interpret the purple area under the curve.

Round to three decimal places.

Provide your answer below:

$\mu_{\overline{x}}=$

x

=hours

$\sigma_{\overline{x}}=$

x

=hours

$P\left(\overline{x}>4.7 ight)=$

P(x>4.7)=