The results of a common standardized test used in psychology research is designed so that the population mean is 160 and the standard deviation is 30. A subject earns a score of 127. What is the Z-score for this raw score? Z-Score =
The results of a common standardized test used in psychology research is designed so that the population mean is 160 and the standard deviation is 30. A subject earns a score of 127. What is the Z-score for this raw score? Z-Score =
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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![**Question:**
The results of a common standardized test used in psychology research is designed so that the population mean is 160 and the standard deviation is 30. A subject earns a score of 127. What is the z-score for this raw score?
**Solution:**
To calculate the z-score, use the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where:
- \(X\) is the raw score,
- \(\mu\) is the population mean,
- \(\sigma\) is the standard deviation.
In this case:
- \(X = 127\),
- \(\mu = 160\),
- \(\sigma = 30\).
Substitute these values into the formula:
\[
z = \frac{(127 - 160)}{30} = \frac{-33}{30} = -1.1
\]
**Answer:**
z-score = -1.1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0645be48-2a82-494d-ae06-198a7d9d9703%2F88054384-787f-4fec-b8ef-dd4e65f037d4%2Fp9qsugn_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
The results of a common standardized test used in psychology research is designed so that the population mean is 160 and the standard deviation is 30. A subject earns a score of 127. What is the z-score for this raw score?
**Solution:**
To calculate the z-score, use the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where:
- \(X\) is the raw score,
- \(\mu\) is the population mean,
- \(\sigma\) is the standard deviation.
In this case:
- \(X = 127\),
- \(\mu = 160\),
- \(\sigma = 30\).
Substitute these values into the formula:
\[
z = \frac{(127 - 160)}{30} = \frac{-33}{30} = -1.1
\]
**Answer:**
z-score = -1.1
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