standardized exam's scores are normally distributed. In a recent year, the mean test score was 1515 and the standard deviation was 316. The test scores of idents selected at random are 1920, 1260, 2260, and 1390. Find the z-scores that correspond to each value and determine whether any of the values are un ne z-score for 1920 is Cound to two decimal places as needed.) ne z-score for 1260 is Round to two decimal places as needed.) he z-score for 2260 is Round to two decimal places as needed.) The z-score for 1390 is Round to two decimal places as needed.) Mhich yoluor if any are unusual? Select the correct choice below and if necessary, fill in the answer box within your choice.
standardized exam's scores are normally distributed. In a recent year, the mean test score was 1515 and the standard deviation was 316. The test scores of idents selected at random are 1920, 1260, 2260, and 1390. Find the z-scores that correspond to each value and determine whether any of the values are un ne z-score for 1920 is Cound to two decimal places as needed.) ne z-score for 1260 is Round to two decimal places as needed.) he z-score for 2260 is Round to two decimal places as needed.) The z-score for 1390 is Round to two decimal places as needed.) Mhich yoluor if any are unusual? Select the correct choice below and if necessary, fill in the answer box within your choice.
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 in Normally Distributed Exam Scores
In a recent exam, a standardized test scores are normally distributed. The mean test score was 1515, and the standard deviation was 316. We will calculate the z-scores for four given student scores: 1920, 1260, 2260, and 1390. Then, we will determine whether any of these scores are unusual.
**Problem Statement:**
Given the following information:
- Mean (μ) = 1515
- Standard Deviation (σ) = 316
Calculate the z-scores for the specified test scores and determine whether any of the values are unusual.
#### Z-Score Formula
The z-score for a data point \( x \) can be calculated using the formula:
\[ z = \frac{x - \mu}{\sigma} \]
where \( x \) is the test score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
#### Calculate Z-Scores
1. **The z-score for 1920 is \( \_\_ \):**
\[ z = \frac{1920 - 1515}{316} \]
(Round to two decimal places as needed.)
2. **The z-score for 1260 is \( \_\_ \):**
\[ z = \frac{1260 - 1515}{316} \]
(Round to two decimal places as needed.)
3. **The z-score for 2260 is \( \_\_ \):**
\[ z = \frac{2260 - 1515}{316} \]
(Round to two decimal places as needed.)
4. **The z-score for 1390 is \( \_\_ \):**
\[ z = \frac{1390 - 1515}{316} \]
(Round to two decimal places as needed.)
#### Determining Unusual Values
Z-scores are considered unusual if they are below -2 or above 2.
**Question: Which values, if any, are unusual? Select the correct choice below:**
- **A.** The unusual value(s) is/are \(\_\_\). (Use a comma to separate answers as needed.)
- **B.** None of the values are unusual.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7511c35-2106-4215-8e3f-fd47bce3a676%2F2e238ead-3b66-4cef-8c63-fd661bbde3ae%2F8j6944o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Z-Scores in Normally Distributed Exam Scores
In a recent exam, a standardized test scores are normally distributed. The mean test score was 1515, and the standard deviation was 316. We will calculate the z-scores for four given student scores: 1920, 1260, 2260, and 1390. Then, we will determine whether any of these scores are unusual.
**Problem Statement:**
Given the following information:
- Mean (μ) = 1515
- Standard Deviation (σ) = 316
Calculate the z-scores for the specified test scores and determine whether any of the values are unusual.
#### Z-Score Formula
The z-score for a data point \( x \) can be calculated using the formula:
\[ z = \frac{x - \mu}{\sigma} \]
where \( x \) is the test score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
#### Calculate Z-Scores
1. **The z-score for 1920 is \( \_\_ \):**
\[ z = \frac{1920 - 1515}{316} \]
(Round to two decimal places as needed.)
2. **The z-score for 1260 is \( \_\_ \):**
\[ z = \frac{1260 - 1515}{316} \]
(Round to two decimal places as needed.)
3. **The z-score for 2260 is \( \_\_ \):**
\[ z = \frac{2260 - 1515}{316} \]
(Round to two decimal places as needed.)
4. **The z-score for 1390 is \( \_\_ \):**
\[ z = \frac{1390 - 1515}{316} \]
(Round to two decimal places as needed.)
#### Determining Unusual Values
Z-scores are considered unusual if they are below -2 or above 2.
**Question: Which values, if any, are unusual? Select the correct choice below:**
- **A.** The unusual value(s) is/are \(\_\_\). (Use a comma to separate answers as needed.)
- **B.** None of the values are unusual.
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