In a normally distributed process, what percent of measurements will fall within +/- 3.0 sigma?

In a normally distributed process, approximately 99.73% of measurements fall within ±3.0 sigma (standard deviations) from the mean. This percentage is derived from the empirical rule, also known as the 68-95-99.7 rule, which states that:

• About 68% of the data falls within 1 standard deviation from the mean.

• Approximately 95% falls within 2 standard deviations.

• Roughly 99.7% falls within 3 standard deviations.

This understanding is fundamental when analyzing process performance, as it indicates that nearly all values in a normal distribution fall within this range, representing the vast majority of expected variations in the process. The significance of this rule is crucial for process control, quality assurance, and understanding how much of the process variation is due to common causes versus special causes.

The other options represent different percentages that do not accurately reflect the measurements associated with ±3.0 sigma in a normal distribution. Specifically, while 95.45% corresponds to a ±2.0 sigma range, 99.99% exceeds the standard figure for ±3.0 sigma, and 100% inaccurately implies that every measurement falls within that range without exception. Hence, the correct answer is