0.674 sd.
95% is within 2 standard deviations of the mean.
99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.
95%
Assuming a normal distribution, Pr { X < -1.33 } ~= 0.091759135650280765 or about 9.18 %
I believe the standard deviations are measured from the median, not the mean.1 Standard Deviation is 34% each side of median, so that is 68% total.2 Standard Deviations is 48% each side of median, so that is 96% total.
95% is within 2 standard deviations of the mean.
99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.
For a normal probability distribution to be considered a standard normal probability distribution, it must have a mean of 0 and a standard deviation of 1. This standardization allows for the use of z-scores, which represent the number of standard deviations a data point is from the mean. Any normal distribution can be transformed into a standard normal distribution through the process of standardization.
95%
about 68%
Assuming a normal distribution, Pr { X < -1.33 } ~= 0.091759135650280765 or about 9.18 %
95 percent of measurements are less than 2 standard deviations away from the mean, assuming a normal distribution.
In a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data is within 1 standard deviation, and about 99.7% is within 3 standard deviations. Therefore, the range within 2 standard deviations captures a significant majority of the data points.
In a standard normal distribution, approximately 95% of the data falls within two standard deviations (±2σ) of the mean (μ). This means that if you take the mean and add or subtract two times the standard deviation, you capture the vast majority of the data points. This property is a key aspect of the empirical rule, which describes how data is spread in a normal distribution.
2.275 %
The probability of the mean plus or minus 1.96 standard deviations is 0. The probability that a continuous distribution takes any particular value is always zero. The probability between the mean plus or minus 1.96 standard deviations is 0.95
I believe the standard deviations are measured from the median, not the mean.1 Standard Deviation is 34% each side of median, so that is 68% total.2 Standard Deviations is 48% each side of median, so that is 96% total.