2.275 %
95 percent of measurements are less than 2 standard deviations away from the mean, assuming a normal distribution.
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
the t distributions take into account the variability of the sample standard deviations. I think that it is now common to use the t distribution when the population standard deviation is unknown, regardless of the sample size.
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
Mean is the average, sum total divided by total number of data entries. Standard deviation is the square root of the sum total of the data values divided by the total number of data values. The standard normal distribution is a distribution that closely resembles a bell curve.
95% is within 2 standard deviations of the mean.
95 percent of measurements are less than 2 standard deviations away from the mean, assuming a normal distribution.
It depends on the shape of the distribution. For standard normal distribution, a two tailed range would be from -1.15 sd to + 1.15 sd.
99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.
in a normal distribution, the mean plus or minus one standard deviation covers 68.2% of the data. If you use two standard deviations, then you will cover approx. 95.5%, and three will earn you 99.7% coverage
0.674 sd.
95%
Assuming a normal distribution, Pr { X < -1.33 } ~= 0.091759135650280765 or about 9.18 %
about 68%
The answer will depend on what the distribution is. Non-statisticians often assum that the variable that they are interested in follows the Standard Normal distribution. This assumption must be justified. If that is the case then the answer is 81.9%
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.