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%
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
95% is within 2 standard deviations of the mean.
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.