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The scores on the SAT verbal test in recent years follow approximately the normal distribution distribution. Students get a mean score of 547 with a standard deviation of 101. Use technology to answer these questions. a. What is the proportion of students scoring under 400 (4 decimal positions)? b. What is the proportion of students scoring between 400 and 550? (4 decimal positions) c. What is the proportion of students scoring over 550? (4 decimal positions) d. How high must a student score to place in the top 10% of all students taking the SAT? State answer as a whole number.

The scores on the SAT verbal test in recent years follow approximately the normal distribution distribution. Students get a mean score of 547 with a standard deviation of 101. Use technology to answer these questions. a. What is the proportion of students scoring under 400 (4 decimal positions)? b. What is the proportion of students scoring between 400 and 550? (4 decimal positions) c. What is the proportion of students scoring over 550? (4 decimal positions) d. How high must a student score to place in the top 10% of all students taking the SAT? State answer as a whole number.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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# Understanding SAT Verbal Test Scores The scores on the SAT verbal test in recent years follow approximately the normal distribution. Students achieve a mean score of 547 with a standard deviation of 101. Use appropriate technology or statistical tools to answer the following questions related to the SAT verbal test scores: ### Questions 1. **What is the proportion of students scoring under 400?** *Provide your answer to 4 decimal positions.* ``` Answer: ___________ ``` 2. **What is the proportion of students scoring between 400 and 550?** *Provide your answer to 4 decimal positions.* ``` Answer: ___________ ``` 3. **What is the proportion of students scoring over 550?** *Provide your answer to 4 decimal positions.* ``` Answer: ___________ ``` 4. **How high must a student score to place in the top 10% of all students taking the SAT?** *State your answer as a whole number.* ``` Answer: ___________ ``` To solve these questions, you will typically use the properties of the normal distribution and tools such as z-scores or statistical software that can handle normal distribution calculations. ### Explanation In a normal distribution model: - **The mean** (average score) tells us where the center of the distribution lies. - **The standard deviation** measures the spread. A larger standard deviation indicates that the scores are more spread out around the mean. For each question, you might: - Compute z-scores to determine the relative position of a specific score. - Use the z-table, or statistical software to find the proportion or percentile corresponding to a z-score. For question (d), to find the score corresponding to the top 10%, you would find the z-score that corresponds to the 90th percentile (since it's top 10%, it means 90% of students scored below this score) and then convert that z-score into an actual SAT score using the mean and standard deviation provided. ### Helpful Tools: - **Z-Score Table:** Converts z-scores to percentiles. - **Statistical Software/Calculators:**Simplify the process of finding proportions under the normal curve. By thoroughly understanding these principles, students can interpret and solve questions involving the normal distribution of SAT scores confidently.
Transcribed Image Text:# Understanding SAT Verbal Test Scores The scores on the SAT verbal test in recent years follow approximately the normal distribution. Students achieve a mean score of 547 with a standard deviation of 101. Use appropriate technology or statistical tools to answer the following questions related to the SAT verbal test scores: ### Questions 1. **What is the proportion of students scoring under 400?** *Provide your answer to 4 decimal positions.* ``` Answer: ___________ ``` 2. **What is the proportion of students scoring between 400 and 550?** *Provide your answer to 4 decimal positions.* ``` Answer: ___________ ``` 3. **What is the proportion of students scoring over 550?** *Provide your answer to 4 decimal positions.* ``` Answer: ___________ ``` 4. **How high must a student score to place in the top 10% of all students taking the SAT?** *State your answer as a whole number.* ``` Answer: ___________ ``` To solve these questions, you will typically use the properties of the normal distribution and tools such as z-scores or statistical software that can handle normal distribution calculations. ### Explanation In a normal distribution model: - **The mean** (average score) tells us where the center of the distribution lies. - **The standard deviation** measures the spread. A larger standard deviation indicates that the scores are more spread out around the mean. For each question, you might: - Compute z-scores to determine the relative position of a specific score. - Use the z-table, or statistical software to find the proportion or percentile corresponding to a z-score. For question (d), to find the score corresponding to the top 10%, you would find the z-score that corresponds to the 90th percentile (since it's top 10%, it means 90% of students scored below this score) and then convert that z-score into an actual SAT score using the mean and standard deviation provided. ### Helpful Tools: - **Z-Score Table:** Converts z-scores to percentiles. - **Statistical Software/Calculators:**Simplify the process of finding proportions under the normal curve. By thoroughly understanding these principles, students can interpret and solve questions involving the normal distribution of SAT scores confidently.
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