What percentages correspond to 1, 2, and 3 standard deviations in a normal distribution?

In a normal distribution, the empirical rule, also known as the 68-95-99.7 rule, describes how data values are distributed within standard deviations from the mean. According to this rule:

• Approximately 68.3% of the data falls within one standard deviation of the mean. This means that if you were to take a sample from this distribution, about 68.3% of the values would lie within this range.

• Approximately 95.5% of the data falls within two standard deviations from the mean. This indicates that a significant majority of values are captured within a broader range around the mean compared to one standard deviation.

• About 99.7% of the data is included within three standard deviations from the mean. This encompasses nearly all of the dataset, illustrating that extreme values beyond this range are quite rare in a normally distributed dataset.

The other choices do not accurately reflect these standard percentage ranges associated with standard deviations. The percentages provided in option B are widely recognized and established in statistics for a normal distribution, making it the correct choice. Understanding this empirical rule is crucial for interpreting data behavior and variability in fields like industrial hygiene, where assessing risk levels and making data-driven decisions are essential.