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. Use Excel to calculate the probability that the sample mean dream length is less than 7 minutes. Round to three decimal places. Provide your answer below: $\mu_{\overline{x}}=$ minutes $\sigma_{\overline{x}}=$ minutes $P\left(\overline{x}<7\right)=$ Formula keypad has been closed. Press Control Backslash to open it again.