In a normal distribution, approximately what percentage of observations fall within one standard deviation from the mean?

In a normal distribution, approximately 68% of the observations fall within one standard deviation (σ) of the mean (μ). This characteristic is a fundamental property of normal distributions and is derived from the empirical rule, also known as the 68-95-99.7 rule.

The empirical rule states that:

1. About 68% of the data lies within one standard deviation of the mean (μ ± σ).

2. About 95% lies within two standard deviations (μ ± 2σ).

3. About 99.7% lies within three standard deviations (μ ± 3σ).

The importance of this rule lies in its ability to summarize the distribution of data in a concise manner, thereby allowing statisticians and data analysts to quickly recognize the spread and concentration of values around the mean. This 68% figure reflects the clustering of data points closely around the mean, which is a characteristic property of normal distributions, as they are symmetric and bell-shaped.

The other percentages provided in the choices represent the coverage within larger intervals (two and three standard deviations), which is not relevant when specifically addressing the range of one standard deviation around the mean.