for a normal curve what percentage of values falls beyond two standard deviations from the mean

http://davidmlane.com/hyperstat/z_table.html

set between -2 to +2 SDeviation, see that it is 95.45 percent

To find the percentage of values that fall beyond two standard deviations from the mean in a normal curve, we can use the empirical rule or the standard normal distribution table.

The empirical rule states that:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.

Based on this rule, we can conclude that approximately 5% of the data falls beyond two standard deviations from the mean in either tail of the normal curve. This 5% is evenly split, with approximately 2.5% beyond the upper end and 2.5% beyond the lower end.

Another approach is to use the standard normal distribution table or a probability density calculator. These tools allow you to find the probabilities associated with different z-scores (standard deviations from the mean). For example:

1. Look up the z-score for two standard deviations (z = 2) in the standard normal distribution table or calculator. This will give you the area under the curve up to that z-score.
2. Subtract the obtained area from 1. Since the area under a normal curve sums up to 1, subtracting the area up to two standard deviations from 1 will give you the area beyond two standard deviations.
3. Multiply the resulting area by 100 to convert it into a percentage.

Using this method, you should find that approximately 2.28% of the values fall beyond two standard deviations from the mean in either tail of the curve.