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Answer :
Final answer:
According to the 68-95-99.7 rule, if a data set has a mean of 6.2 and a standard deviation of 0.9, 68% of the observations would fall between 5.3 and 7.1.
Explanation:
The 68-95-99.7 rule, also known as the empirical rule, is a guideline in statistics that applies to data that is normally distributed. This rule states that approximately 68% of all data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this particular problem, the mean (µ) is 6.2 and the standard deviation (σ) is 0.9. So, if we use the 68% rule, we can calculate the range where we expect 68% of observations to fall. We do this by subtracting and adding the standard deviation from/to the mean.
Therefore, 68% of the observations should fall between 6.2 - 0.9 = 5.3 and 6.2 + 0.9 = 7.1.
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