Approximately what percentage of observations in a normal distribution fall within one standard deviation of the mean?

In a normal distribution, about 68% of the observations fall within one standard deviation of the mean. This characteristic is fundamentally linked to the properties of the normal distribution, which is a symmetric, bell-shaped curve centered around the mean. The empirical rule, also known as the 68-95-99.7 rule, specifies that:

• Approximately 68% of values lie within one standard deviation from the mean.

• Around 95% of values fall within two standard deviations.

• About 99.7% of values are found within three standard deviations.

This statistical property is crucial for hypothesis testing, confidence interval estimation, and various other applications in statistics. It allows statisticians to make inferences about a population based on sample data, assuming the underlying distribution is normal. Understanding this concept helps in recognizing the variability and distribution of data points around the mean in a normal context.