The answer depends on the degrees of freedom (df). If the df > 1 then the mean is 0, and the standard deviation, for df > 2, is sqrt[df/(df - 2)].
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T-scores have a mean of 50 and a standard deviation of 10. These values are fixed and do not change regardless of the distribution of T-scores.
It depends on what the distribution is. In a Normal or Gaussian distribution, the standard deviation is the square root of the mean, so it could be 3.1 but, again, it depends on the distribution.
The statement is probably: The mean and standard deviation of a distribution are 55 and 4.33 respectively.
It is any standardised distribution.
with mean of and standard deviation of 1.
standard normal