For a normal curve, what percentage of values falls beyond two standard deviations from the mean?
I think you can easily get your answer here:
http://davidmlane.com/hyperstat/z_table.html
Read from the following table:
https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf
You will see that 2.275% of data falls beyond μ+2σ and another 2.275% of data falls below μ-2σ.
To determine the percentage of values that fall beyond two standard deviations from the mean in a normal curve, you can use the empirical rule, also known as the 68-95-99.7 rule.
According to the empirical rule, for a normal distribution:
- Approximately 68% of the values fall within one standard deviation from the mean.
- Approximately 95% of the values fall within two standard deviations from the mean.
- Approximately 99.7% of the values fall within three standard deviations from the mean.
Since we want to find the percentage of values that fall beyond two standard deviations from the mean, we can subtract the percentage within two standard deviations from 100%.
Therefore, the percentage of values that fall beyond two standard deviations from the mean in a normal curve is approximately 100% - 95% = 5%.