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The standard normal distribution is a normal distribution with mean 0 and variance 1.
le standard normal distribution is a normal distribution who has mean 0 and variance 1
When its probability distribution the standard normal distribution.
The Normal distribution is, by definition, symmetric. There is no other kind of Normal distribution, so the adjective is not used.
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.