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Q: What is the mean and standard deviations and the standard normal distribution?

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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.

0.674 sd.

95 percent of measurements are less than 2 standard deviations away from the mean, assuming a normal distribution.

95%

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

2.275 %

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.

The mean of a standard normal distribution is 0.

The standard normal distribution has a mean of 0 and a standard deviation of 1.

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.

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