It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately Normally distributed with 375 minutes and standard deviation 65minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with 530 minutes and standard deviation 109 minutes. A researcher records the minutes of activity for an SRS of 55 mildly obese people and an SRS of 55 lean people. James A. Levine et al., "Inter-individual variation in posture allocation: Possible role in human obesity," Science, 307 (2005), pp. 584-586.     What is the probability that the mean number of minutes of daily activity of the 55 lean people exceeds 410 minutes? Give your answer to four decimal places. What is the probability ?

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