What percentage of observations falls within one standard deviation from the mean in a normal distribution?

What percentage of observations falls within one standard deviation from the mean in a normal distribution?

• A. 65%
• B. 68%
• C. 70%
• D. 72%

Answer: (B)

In a normal distribution, the empirical rule, also known as the 68-95-99.7 rule, states that approximately 68% of the observations fall within one standard deviation from the mean. This characteristic of normal distributions allows for predictions about data tendencies based on how spread out the data points are relative to the mean. The reason why this percentage is specifically 68% can be attributed to the shape and properties of the normal distribution curve. This bell-shaped curve is symmetric around the mean, meaning that the data is equally likely to fall above or below the mean. As such, when you calculate the area under the curve within one standard deviation on either side of the mean, it accounts for about 68% of the total area under the curve, indicating that this proportion of observations is expected to lie within that range. This principle is fundamental in statistics, as it provides a quick way to understand the distribution of data and is widely used in various applications, including quality control, finance, and research.

In a normal distribution, the empirical rule, also known as the 68-95-99.7 rule, states that approximately 68% of the observations fall within one standard deviation from the mean. This characteristic of normal distributions allows for predictions about data tendencies based on how spread out the data points are relative to the mean.

The reason why this percentage is specifically 68% can be attributed to the shape and properties of the normal distribution curve. This bell-shaped curve is symmetric around the mean, meaning that the data is equally likely to fall above or below the mean. As such, when you calculate the area under the curve within one standard deviation on either side of the mean, it accounts for about 68% of the total area under the curve, indicating that this proportion of observations is expected to lie within that range.

This principle is fundamental in statistics, as it provides a quick way to understand the distribution of data and is widely used in various applications, including quality control, finance, and research.