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post 1

My analysis of the empirical rule will be focused on heights of students at school. Assume that student heights are distributed with an assumed mean of 1.4 and an assumed standard deviation of 0.15. This data can use the empirical rule because it is normally distributed, or symmetrical.

68% of the data falls between 1.25m and 1.55m

95% of the data falls between 1.1m and 1.7m

99.7% of the data falls between 0.95m and 1.85m

This tells us that 68% of the data, 1.25m - 1.55m is closest to the mean while the majority of values will be more spread out, being within 3 standard deviations of the mean.

post 2

For this discussion on the empirical rule, we can look at SAT scores. Let's assume the mean SAT score is 1150 and the standard deviation is 150. This data is normally distributed. 68% of SAT scores are between 1000 and 1300 which is one standard deviation of the mean. 95% of SAT scores are between 850 and 1450, making it 2 standard deviations of the mean. Around 99.7% of scores are between 700 and 1600, so 3 standard deviations of the mean. When looking at this data, people evaluating can see that the 68% of the scores are closest to the mean and the other data gets more distant from there.