On a recent quiz, the class mean was 76 with a standard deviation of 4.8. Calculate the z-score (to 4 decimal places) for a person who received score of 79. z-score: Is this unusual? O Unusual O Not Unusual
On a recent quiz, the class mean was 76 with a standard deviation of 4.8. Calculate the z-score (to 4 decimal places) for a person who received score of 79. z-score: Is this unusual? O Unusual O Not Unusual
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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![### Z-Score Calculation and Analysis
#### Problem Statement:
On a recent quiz, the class mean was 76 with a standard deviation of 4.8. Calculate the z-score (to 4 decimal places) for a person who received a score of 79.
#### Calculation of Z-Score:
To find the z-score, use the following formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( X \) is the score,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.
For this problem:
- Mean (\( \mu \)) = 76
- Standard Deviation (\( \sigma \)) = 4.8
- Score (\( X \)) = 79
**Formula Application:**
\[ z = \frac{(79 - 76)}{4.8} = \frac{3}{4.8} = 0.6250 \]
Enter the z-score in the provided input box.
**Z-Score Input Box:**
\[ \text{z-score:} \ \_\_\_\_\_\_ \]
#### Analysis:
Evaluate if the score is unusual by comparing the z-score with typical z-score thresholds. Generally, in a normal distribution:
- A z-score less than -2 or greater than +2 is considered unusual.
#### Decision:
- Check the appropriate option based on the calculated z-score.
**Options:**
- Unusual
- Not Unusual
Given the calculated z-score of 0.6250, you should select "Not Unusual."
#### Diagram/Graph Explanation:
There are no diagrams or graphs associated with this text.
Feel free to utilize this as a guiding example to understand and calculate z-scores as well as analyze the results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbed7ab37-3726-4b83-a741-6ed60a3ee8a9%2Fbdfd255e-a22a-4818-91ce-08cf52c7ed9e%2Fxyrc6yn_processed.png&w=3840&q=75)
Transcribed Image Text:### Z-Score Calculation and Analysis
#### Problem Statement:
On a recent quiz, the class mean was 76 with a standard deviation of 4.8. Calculate the z-score (to 4 decimal places) for a person who received a score of 79.
#### Calculation of Z-Score:
To find the z-score, use the following formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( X \) is the score,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.
For this problem:
- Mean (\( \mu \)) = 76
- Standard Deviation (\( \sigma \)) = 4.8
- Score (\( X \)) = 79
**Formula Application:**
\[ z = \frac{(79 - 76)}{4.8} = \frac{3}{4.8} = 0.6250 \]
Enter the z-score in the provided input box.
**Z-Score Input Box:**
\[ \text{z-score:} \ \_\_\_\_\_\_ \]
#### Analysis:
Evaluate if the score is unusual by comparing the z-score with typical z-score thresholds. Generally, in a normal distribution:
- A z-score less than -2 or greater than +2 is considered unusual.
#### Decision:
- Check the appropriate option based on the calculated z-score.
**Options:**
- Unusual
- Not Unusual
Given the calculated z-score of 0.6250, you should select "Not Unusual."
#### Diagram/Graph Explanation:
There are no diagrams or graphs associated with this text.
Feel free to utilize this as a guiding example to understand and calculate z-scores as well as analyze the results.
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