6. A population of scores has u = 44. In this population, a score of X = 40 corresponds to z =-0.50. What is the population standard deviation?
6. A population of scores has u = 44. In this population, a score of X = 40 corresponds to z =-0.50. What is the population 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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![**Question 6:**
A population of scores has a mean (\(\mu\)) of 44. In this population, a score of \(X = 40\) corresponds to a z-score of \(z = -0.50\). What is the population standard deviation?
**Explanation:**
This question involves finding the population standard deviation using the given mean, raw score, and z-score. The z-score formula is:
\[ z = \frac{X - \mu}{\sigma} \]
Where:
- \( z \) is the z-score,
- \( X \) is the raw score,
- \( \mu \) is the mean of the population,
- \( \sigma \) is the population standard deviation.
In this case:
- \(\mu = 44\),
- \(X = 40\),
- \(z = -0.50\).
You can solve for the standard deviation \(\sigma\) by rearranging the formula:
\[ \sigma = \frac{X - \mu}{z} \]
Substitute the known values to find \(\sigma\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b3063ed-b002-41de-a183-fb693be67884%2Fd2253609-a28d-4e1b-a26b-8345ae39fd79%2Fu3oyngf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6:**
A population of scores has a mean (\(\mu\)) of 44. In this population, a score of \(X = 40\) corresponds to a z-score of \(z = -0.50\). What is the population standard deviation?
**Explanation:**
This question involves finding the population standard deviation using the given mean, raw score, and z-score. The z-score formula is:
\[ z = \frac{X - \mu}{\sigma} \]
Where:
- \( z \) is the z-score,
- \( X \) is the raw score,
- \( \mu \) is the mean of the population,
- \( \sigma \) is the population standard deviation.
In this case:
- \(\mu = 44\),
- \(X = 40\),
- \(z = -0.50\).
You can solve for the standard deviation \(\sigma\) by rearranging the formula:
\[ \sigma = \frac{X - \mu}{z} \]
Substitute the known values to find \(\sigma\).
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