It's the same as a z-Transformation.
for all xi: (xi-mean(x)) / std(x)
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The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
The standard normal curve is symmetrical.
The standard normal distribution is a normal distribution with mean 0 and variance 1.
A mathematical definition of a standard normal distribution is given in the related link. A standard normal distribution is a normal distribution with a mean of 0 and a variance of 1.
the standard normal curve 2