n a normal distribution, what percentage of data falls within one standard deviation of the mean? 25% 50% 68% 95.5%

Break Down the Problem

1. Identify the properties of a normal distribution.
2. Determine the percentage of the data that falls within one standard deviation from the mean.

Relevant Concepts

• In a normal distribution, the empirical rule (also known as the 68-95-99.7 rule) states:
  • Approximately 68% of the data falls within one standard deviation of the mean.

Analysis and Detail

1. Understanding Standard Deviation: A standard deviation measures the amount of variation or dispersion in a set of values. In a normal distribution:
   • 68% of the observations lie within one standard deviation (σ) from the mean (µ).
   • This means that for a normally distributed dataset, if you start at the mean and move one standard deviation to the left and one standard deviation to the right, you encompass about 68% of the total data.

Verify and Summarize

The correct answer for the percentage of data that falls within one standard deviation of the mean in a normal distribution is confirmed as follows:

• According to the empirical rule:
  • 68% of the data lies within the range (µ - σ, µ + σ).

Final Answer

The percentage of data that falls within one standard deviation of the mean in a normal distribution is 68%.