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 65 minutes. 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 mildly obese people exceeds 410 minutes? Give your answer to four decimal places.
What is the probability ?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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