A psychologist believes a majority of people have dreams that last less than 7 minutes. Assume that the length of a dream follows an unknown distribution with a mean of 6 minutes and a standard deviation of 2.4 minutes. The psychologist randomly selects 31 people for a sleep study and measures the length of each of their dreams. What is the probability that the sample mean dream length is less than 7 minutes? 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 x and x; Calculate the z-score for x=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 to three decimal places