Which statement correctly describes the Empirical Rule for bell-shaped distributions?

The statement that approximately 68% of data falls within one standard deviation of the mean is an essential aspect of the Empirical Rule, also known as the 68-95-99.7 rule, which applies to normally distributed data. This rule helps in understanding the distribution of data within a bell-shaped curve—indicating that if one considers a normal distribution, about 68% of observations lie within one standard deviation (σ) from the mean (μ), which implies that this range captures a significant majority of the data points.

The 68% within one standard deviation is critical for making inferences about the data, enabling analysts to assess variability and concentration of observations around the mean. This concept is foundational in statistics and aids in identifying patterns, conducting hypothesis tests, and making predictions about future data based on the normal distribution.

The other options are less accurate interpretations of the Empirical Rule. It does not specify that exactly 50% of data is within one standard deviation of the mean, nor does it assert that all data points must fall within three standard deviations (though 99.7% do fall within that range). Additionally, outliers are generally determined by being beyond a certain number of standard deviations from the mean, and defining them strictly