Q: In a standard normal distribution 95 percent of the data is within plus standard deviations of the mean?

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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.

0.674 sd.

95%

Assuming a normal distribution, Pr { X < -1.33 } ~= 0.091759135650280765 or about 9.18 %

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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.

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.