Understanding Z-Scores What is the z-score of x = 2 if it is 2.8 standard deviations to the left of the mean? What is the z-score of x = 10 if it is 2.4 standard deviations to the right of the mean? 2 =
Understanding Z-Scores What is the z-score of x = 2 if it is 2.8 standard deviations to the left of the mean? What is the z-score of x = 10 if it is 2.4 standard deviations to the right of the mean? 2 =
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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![### Understanding Z-Scores
#### Problem 1:
**Question:** What is the z-score of \( x = 2 \) if it is 2.8 standard deviations to the left of the mean?
**Answer field:**
\[ z = \]
#### Problem 2:
**Question:** What is the z-score of \( x = 10 \) if it is 2.4 standard deviations to the right of the mean?
**Answer field:**
\[ z = \]
**Explanation:**
A z-score is a statistical measurement that describes a value's position relative to the mean of a group of values. It's measured in terms of standard deviations from the mean. The formula to calculate the z-score is given by:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( z \) is the z-score,
- \( X \) is the value,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.
In these problems, we are given the number of standard deviations rather than the raw value \( X \), and we need to find the z-scores.
**For Problem 1:**
Since the value \( x = 2 \) is 2.8 standard deviations to the left of the mean, the z-score is:
\[ z = -2.8 \]
**For Problem 2:**
Since the value \( x = 10 \) is 2.4 standard deviations to the right of the mean, the z-score is:
\[ z = 2.4 \]
These z-scores can help us understand how far a value is from the mean in a standardized manner.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa81afcb-79d6-433d-9647-f14beb19ad20%2F6f6e7df7-286e-44dd-8fbb-3a183b914d92%2F994bew_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Z-Scores
#### Problem 1:
**Question:** What is the z-score of \( x = 2 \) if it is 2.8 standard deviations to the left of the mean?
**Answer field:**
\[ z = \]
#### Problem 2:
**Question:** What is the z-score of \( x = 10 \) if it is 2.4 standard deviations to the right of the mean?
**Answer field:**
\[ z = \]
**Explanation:**
A z-score is a statistical measurement that describes a value's position relative to the mean of a group of values. It's measured in terms of standard deviations from the mean. The formula to calculate the z-score is given by:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( z \) is the z-score,
- \( X \) is the value,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.
In these problems, we are given the number of standard deviations rather than the raw value \( X \), and we need to find the z-scores.
**For Problem 1:**
Since the value \( x = 2 \) is 2.8 standard deviations to the left of the mean, the z-score is:
\[ z = -2.8 \]
**For Problem 2:**
Since the value \( x = 10 \) is 2.4 standard deviations to the right of the mean, the z-score is:
\[ z = 2.4 \]
These z-scores can help us understand how far a value is from the mean in a standardized manner.
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