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d) A students with a score higher than 50% of those taking the exam has a score of... e) A students with a score at the 80th percentile has a score of...

d) A students with a score higher than 50% of those taking the exam has a score of... e) A students with a score at the 80th percentile has a score of...

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
Problem 1P
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I just need help with parts D and E please.

**Title: Understanding Normal Distribution in Mathematics Exam Scores** --- **Introduction** Scores on a mathematics exam given to ten-year-old children throughout Japan are normally distributed. The mean score is 520, with a standard deviation of 50. This section will explore how to calculate the proportions and scores based on the normal distribution. --- **Questions and Solutions** a) **What proportion of students have a score between 520 and 593?** To calculate this, you would use a standard normal distribution table or a calculator with statistical functions. Calculate the z-scores for 520 and 593 and find the area under the normal curve between these two points. **Answer: _________** b) **What proportion of students have a score above 477?** Determine the z-score for 477 and use the normal distribution table or calculator to find the area to the right of this score. **Answer: _________** c) **What proportion of students have a score below 456?** Calculate the z-score for 456 and find the area to the left using the normal distribution. **Answer: _________** d) **A student with a score higher than 50% of those taking the exam has a score of...** Since the mean score represents the 50th percentile in a normal distribution, this score is 520. **Answer: ____520____** e) **A student with a score at the 80th percentile has a score of...** Determine the z-score corresponding to the 80th percentile and convert it back to the original score using the mean and standard deviation. **Answer: _________** --- **Conclusion** Understanding the distribution of exam scores helps educators and statisticians assess student performance. By using z-scores and the properties of the normal distribution, we can interpret various statistics and make informed decisions regarding educational standards and strategies.
Transcribed Image Text:**Title: Understanding Normal Distribution in Mathematics Exam Scores** --- **Introduction** Scores on a mathematics exam given to ten-year-old children throughout Japan are normally distributed. The mean score is 520, with a standard deviation of 50. This section will explore how to calculate the proportions and scores based on the normal distribution. --- **Questions and Solutions** a) **What proportion of students have a score between 520 and 593?** To calculate this, you would use a standard normal distribution table or a calculator with statistical functions. Calculate the z-scores for 520 and 593 and find the area under the normal curve between these two points. **Answer: _________** b) **What proportion of students have a score above 477?** Determine the z-score for 477 and use the normal distribution table or calculator to find the area to the right of this score. **Answer: _________** c) **What proportion of students have a score below 456?** Calculate the z-score for 456 and find the area to the left using the normal distribution. **Answer: _________** d) **A student with a score higher than 50% of those taking the exam has a score of...** Since the mean score represents the 50th percentile in a normal distribution, this score is 520. **Answer: ____520____** e) **A student with a score at the 80th percentile has a score of...** Determine the z-score corresponding to the 80th percentile and convert it back to the original score using the mean and standard deviation. **Answer: _________** --- **Conclusion** Understanding the distribution of exam scores helps educators and statisticians assess student performance. By using z-scores and the properties of the normal distribution, we can interpret various statistics and make informed decisions regarding educational standards and strategies.
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