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I'm sure there are plenty of people here that know about z-scores. Do you have a particular question?
Can you have the same z score in the same set of data? I'm thinking yes because what if you have the same number more than once but not sure
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If you know the mean and standard deviation, then you can plug them into
\[z = (x - \mu)/\sigma,\]
wnere mu is the mean and sigma is the standard deviation. Then the probability distribution in x becomes the standard normal distribution in z.
If you are given a set of data, you can get their sample mean and sample variance, using the formula for a discrete set of data.
If the number of data points is at least thiryt, then the normal approximation to distribution due to the data will be a good approximation.