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 365365 minutes and standard deviation 6969 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with 528528 minutes and standard deviation 106106 minutes. A researcher records the minutes of activity for an SRS of 66 mildly obese people and an SRS of 66 leanpeople.

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 66 mildly obese people exceeds 420minutes?420minutes? Give your answer to four decimalplaces.