The standard normal distribution has mean 0 and variance 1. It is not clear what 0.62 has to do with the distribution.
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The standard deviation in a standard normal distribution is 1.
The standard deviation in a standard normal distribution is 1.
The standard normal distribution is a special case normal distribution, which has a mean of zero and a standard deviation of one.
Yes, the normal distribution, standard or not is always continuous.
The mean of a standard normal distribution is 0.