If the mean score on the final exam is 70 with a standard deviation of 10 then the test score of a student that had a z-score of -1.5 is: 55 60 75 85
If the mean score on the final exam is 70 with a standard deviation of 10 then the test score of a student that had a z-score of -1.5 is: 55 60 75 85
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:**
If the mean score on the final exam is 70 with a standard deviation of 10, then the test score of a student that had a z-score of -1.5 is:
**Options:**
- ○ 55
- ○ 60
- ○ 75
- ○ 85
To answer this question, recall the formula for calculating a z-score:
\[ Z = \frac{X - \mu}{\sigma} \]
Where:
- \( Z \) = z-score
- \( X \) = raw score
- \( \mu \) = mean
- \( \sigma \) = standard deviation
Rearrange the formula to solve for the raw score \( X \):
\[ X = Z \cdot \sigma + \mu \]
Given:
- \( Z = -1.5 \)
- \( \mu = 70 \)
- \( \sigma = 10 \)
Plug these values into the formula:
\[ X = (-1.5) \cdot 10 + 70 \]
\[ X = -15 + 70 \]
\[ X = 55 \]
Thus, the correct test score of a student with a z-score of -1.5 is:
- ○ **55**
- ○ 60
- ○ 75
- ○ 85](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F511cca5e-35a6-4593-89c5-a187014510b0%2F80251383-854d-4129-97a7-72f4d55a4793%2F6k1s47n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
If the mean score on the final exam is 70 with a standard deviation of 10, then the test score of a student that had a z-score of -1.5 is:
**Options:**
- ○ 55
- ○ 60
- ○ 75
- ○ 85
To answer this question, recall the formula for calculating a z-score:
\[ Z = \frac{X - \mu}{\sigma} \]
Where:
- \( Z \) = z-score
- \( X \) = raw score
- \( \mu \) = mean
- \( \sigma \) = standard deviation
Rearrange the formula to solve for the raw score \( X \):
\[ X = Z \cdot \sigma + \mu \]
Given:
- \( Z = -1.5 \)
- \( \mu = 70 \)
- \( \sigma = 10 \)
Plug these values into the formula:
\[ X = (-1.5) \cdot 10 + 70 \]
\[ X = -15 + 70 \]
\[ X = 55 \]
Thus, the correct test score of a student with a z-score of -1.5 is:
- ○ **55**
- ○ 60
- ○ 75
- ○ 85
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