Stats Z score question

Question

What is the Z score for any mean? What is the z score for any standard deviation?

Answer 1

the z score for any mean = 0

z score is the value minus the mean all divided by the standard deviation

mean minus mean = 0, so the z score is 0/sd = 0 for any sd unless sd=0, then z score is undefined, as sd=0 means all scores are = mean

z score for a value = one standard deviation from the mean is 1 or -1, depending on whether the value > or < the mean.

z score for a value = two standard deviations above the mean is 2, two standard deviations below the mean the z score = -2

how ever many standard deviations from the mean the value is, that's the z-score.

Answer 2

z-score for an individual value from a sample, population mean and standard deviation:

z score = (individual value - population mean)/population standard deviation

z-score for an individual sample mean, population mean and standard deviation:

z-score = (sample mean - population mean)/(population standard deviation/SQRT(sample size))