In a normally distributed variable, what percentage of values falls within one standard deviation of the mean?

In a normally distributed variable, what percentage of values falls within one standard deviation of the mean?

• A. 50%
• B. 68%
• C. 75%
• D. 95%

Answer: (B)

In a normally distributed variable, approximately 68% of the values fall within one standard deviation of the mean. This is a fundamental characteristic of the normal distribution, often referred to as the empirical rule or the 68-95-99.7 rule. This rule states that: - About 68% of the data falls within one standard deviation from the mean, - About 95% falls within two standard deviations, - And about 99.7% falls within three standard deviations. This property is integral to understanding normal distributions and is often used in statistical analysis to determine the typical range of values for a data set. It underscores the idea that most of the data in a normal distribution is concentrated around the mean, with fewer values found as you move away from the center. Therefore, knowing that 68% of the data points are clustered within one standard deviation helps in making inferences about the likelihood of a value falling within that range.

In a normally distributed variable, approximately 68% of the values fall within one standard deviation of the mean. This is a fundamental characteristic of the normal distribution, often referred to as the empirical rule or the 68-95-99.7 rule. This rule states that:

• About 68% of the data falls within one standard deviation from the mean,

• About 95% falls within two standard deviations,

• And about 99.7% falls within three standard deviations.

This property is integral to understanding normal distributions and is often used in statistical analysis to determine the typical range of values for a data set. It underscores the idea that most of the data in a normal distribution is concentrated around the mean, with fewer values found as you move away from the center. Therefore, knowing that 68% of the data points are clustered within one standard deviation helps in making inferences about the likelihood of a value falling within that range.