6. What is the Z score for any mean? What is the z score for any standard deviation?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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6. What is the Z score for any mean? What is the z score for any standard deviation?
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Expert Solution

Step 1
Let's consider for 1 st part.
The Z-score is a measure of how many standard deviations a data point is from the mean of a distribution. A Z-score of 0 corresponds to the mean of the distribution, and a Z-score of 1 corresponds to one standard deviation above the mean. Simply it follows N(0, 1) .
Generally, the formula for calculating the Z-score for a given data point x in a normal distribution with mean μ and standard deviation σ is:
Z = (x - μ) / σ
Therefore, the Z-score for any mean μ is 0, since a data point with the same value as the mean has a Z-score of 0.
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