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
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Chapter1: Starting With Matlab
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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
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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