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A z-score gives the distance (specifically number of standard deviations) from the mean so when you compare z-scores, it gives a direct comparison of how far from the mean the values are.

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Q: Why are standard z values so important?
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What is the z-values associated with the middle 44 percent of the standard normal distribution?

-0.772 < Z < 0.772


How do you find a z-score?

Z Score is (x-mu)/sigma. The Z-Score allows you to go to a standard normal distribution chart and to determine probabilities or numerical values.


What does a z-score of -1.5 mean?

z-score of a value=(that value minus the mean)/(standard deviation). So a z-score of -1.5 means that a value is 1.5 standard deviations below the mean.


Is the standard normal curve is between Z -3.00 and Z 3.00?

Your question is confusing. However, I will answer the following question, and if this is not your question, please re-submit What is the area under the standard normal curve for z = -3 to Z = 3? The standard normal has a mean of zero and standard deviation of 1. The answer is: 0.9973 This is the equivalent of saying the probability of Z in the range of -3 to +3 is 0.9973 and above 3 it is 0.0027/2 or 0.00135 and below -3 it is 0.00135. Values of the normal distribution can be found in the Internet and textbooks on statistics.


How do you find the number z such that 93 percent of all observations from a standard Normal distribution are greater than z?

The tables for Z-scores are given in the form of P = Prob(Z < z) for various value of P and z. Since Prob(Z > z) = 0.93 > 0.5, then by symmetry, z < 0. So suppose z = -a where a > 0 Now Prob(Z > -a) = 0.93 is the same as Prob(Z < a) = 0.93 [because the standard Normal is symmetric]. therefore, from the tables, a = 1.4758 (approx) and so z = -1.4758 (approx).