What does the 68-95-99.7 rule imply about data in a normal distribution?

The 68-95-99.7 rule, also known as the empirical rule, describes how data is distributed in a normal distribution. According to this rule, approximately 68% of the data values fall within one standard deviation of the mean. This reflects the fact that in a normal distribution, most of the data clusters around the mean, and as you move away from the mean, the number of occurrences diminishes.

This concept is foundational in statistics as it helps in understanding the spread and dispersion of data points in a normal distribution. The significance of the 68% figure is particularly important because it allows for quick assessments of data variability and helps in making inferences about the population based on sample data.

In contrast, the other choices either misrepresent the standard deviations associated with their respective percentages or incorrectly describe how the data is organized around the mean in a normal distribution. Understanding the 68-95-99.7 rule aids in grasping the properties of normal distribution, which is crucial for performing statistical analyses in various settings, including business statistics.