I believe the standard deviations are measured from the median, not 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 %
95% is within 2 standard deviations of the mean.
0.674 sd.
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 %
about 68%
95% is within 2 standard deviations of the mean.
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
When using Chebyshev's Theorem the minimum percentage of sample observations that will fall within two standard deviations of the mean will be __________ the percentage within two standard deviations if a normal distribution is assumed Empirical Rule smaller than greater than the same as
0.674 sd.
95 percent of measurements are less than 2 standard deviations away from the mean, assuming a normal distribution.
2.275 %
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.
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.