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Given a random variable X with mean M and standard deviation S, Z = (X - M)/S
A z-score cannot help calculate standard deviation. In fact the very point of z-scores is to remove any contribution from the mean or standard deviation.
When you don't have the population standard deviation, but do have the sample standard deviation. The Z score will be better to do as long as it is possible to do it.
A negative Z-Score corresponds to a negative standard deviation, i.e. an observation that is less than the mean, when the standard deviation is normalized so that the standard deviation is zero when the mean is zero.
standard deviation
Because the z-score table, which is heavily related to standard deviation, is only applicable to normal distributions.
z-score of a value=(that value minus the mean)/(standard deviation)
z-score of a value=(that value minus the mean)/(standard deviation)
z-score of a value=(that value minus the mean)/(standard deviation)
Z-score is the x value minus the mean, all divided by the standard deviation; or z=(x-mu)/sigma. The "x" value needs to be given to answer the question.
1.41
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution