A range of three standard deviations on either side of the mean covers what percentage of observations?

A range of three standard deviations on either side of the mean covers what percentage of observations?

• A. 95%
• B. 97.5%
• C. 99%
• D. 99.7%

Answer: (D)

The percentage of observations that fall within a range of three standard deviations from the mean in a normal distribution is known as the empirical rule or the 68-95-99.7 rule. According to this rule, approximately 68% of observations fall within one standard deviation, about 95% fall within two standard deviations, and around 99.7% fall within three standard deviations. This means that if you calculate the mean and then move three standard deviations in both the positive and negative direction, you will encompass about 99.7% of the total observations in the dataset. This principle is foundational in statistics, particularly when dealing with normally distributed data, as it helps to understand the spread and concentration of data points. The other options provide percentages that correspond to different ranges of standard deviations. For instance, 95% refers to the percentage of data that lies within two standard deviations, and 97.5% is associated with one-sided tests or confidence intervals that aren't relevant in this specific context of capturing the full range within three standard deviations. The 99% figure, while close, still does not accurately reflect the full range expected in the three standard deviation structure outlined by the empirical rule. Therefore, the understanding of the normal distribution and empirical

The percentage of observations that fall within a range of three standard deviations from the mean in a normal distribution is known as the empirical rule or the 68-95-99.7 rule. According to this rule, approximately 68% of observations fall within one standard deviation, about 95% fall within two standard deviations, and around 99.7% fall within three standard deviations.

This means that if you calculate the mean and then move three standard deviations in both the positive and negative direction, you will encompass about 99.7% of the total observations in the dataset. This principle is foundational in statistics, particularly when dealing with normally distributed data, as it helps to understand the spread and concentration of data points.

The other options provide percentages that correspond to different ranges of standard deviations. For instance, 95% refers to the percentage of data that lies within two standard deviations, and 97.5% is associated with one-sided tests or confidence intervals that aren't relevant in this specific context of capturing the full range within three standard deviations. The 99% figure, while close, still does not accurately reflect the full range expected in the three standard deviation structure outlined by the empirical rule. Therefore, the understanding of the normal distribution and empirical