What percent of measurements falls within +/- 4.5 sigma in a normal distribution?

In a normal distribution, the concept of sigma (σ) represents standard deviations away from the mean. When analyzing how much of the data falls within a specific range of standard deviations, you can apply the empirical rule (also known as the 68-95-99.7 rule) for 1, 2, and 3 standard deviations. However, when evaluating 4.5 standard deviations, this goes beyond the typical parameters of the empirical rule.

Statistical tables for the normal distribution or calculations using the cumulative distribution function indicate that approximately 99.99966% of measurements fall within +/- 4.5 sigma. This means that as you expand the range to 4.5 standard deviations, you capture nearly all of the data points from a normal distribution, which illustrates its high degree of concentration around the mean. As standard deviation increases, the area under the curve accumulates more of the total probability, leading to this extremely high percentage.

This option is not merely an extrapolation but rather based on established statistical principles, confirming that nearly all values in a normally distributed dataset will lie within that range. Therefore, the correct answer represents a comprehensive understanding of data distribution properties in statistics.