What is the empirical rule in relation to the standard normal curve?

The empirical rule, often referred to as the 68-95-99.7 rule, is a statistical guideline that describes how the values in a normal distribution are spread out in relation to the mean and standard deviations. The rule states that in a normal distribution:

• Approximately 68% of the data falls within one standard deviation from the mean (between -1 and 1 standard deviations).
• About 95% of the data lies within two standard deviations from the mean (between -2 and 2 standard deviations).

• Roughly 99.7% of the data is found within three standard deviations from the mean (between -3 and 3 standard deviations).

The correct answer highlights that 99.7% of the area under the standard normal curve is indeed contained between -3 and 3 standard deviations. This illustrates how data is concentrated around the mean in a bell-shaped curve, a fundamental characteristic of normal distributions.

The other statements reflect correct applications of the empirical rule; however, choosing just one answer may lead to overlooking the completeness of the empirical rule itself, which encompasses all these percentages. The best choice acknowledges that all three aspects are critical for understanding the distribution of data in a normal setting.