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
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A
Le
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6. What is the Z score for any mean? What is the z score for any standard deviation?
1,433
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0
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MacBook Air
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Transcribed Image Text:A Le esc 6. What is the Z score for any mean? What is the z score for any standard deviation? 1,433 F1 A BLO @ F2 wie numerical value of the SCULC #C 80 F3 S 111 a F4 % 0 F5 MacBook Air A C FEB 11 F6
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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