For a normal distribution, what percentage of a population is included within two standard deviations of the mean?

• A. 68%
• B. 75%
• C. 95%
• D. 99%

Answer: (C)

In a normal distribution, a well-established statistical rule, known as the empirical rule or the 68-95-99.7 rule, states that approximately 95% of the data falls within two standard deviations of the mean. This rule illustrates how data points are spread out in a bell-shaped curve, which is characteristic of a normal distribution.

When considering only two standard deviations from the mean, both the lower and upper limits encompass a substantial part of the dataset — specifically, it captures most outcomes that are likely to occur in a normally distributed dataset. Thus, this 95% inclusion within two standard deviations is essential for understanding probabilities related to the distribution.

In contrast, the other options reflect different percentages associated with the distribution. For instance, 68% of the data lies within one standard deviation from the mean, while approximately 99.7% of the data can be found within three standard deviations of the mean. The 75% figure does not correlate with standard deviations in a normal distribution, as it does not align with the common empirical rules for spread. This understanding of the percentages is crucial when analyzing data within the context of quality management and other fields that rely on statistical analysis.