E)Use the empirical rule to approximate the percentage of people who take the SAT that will have a mathematics SAT score at least 397. ---### Understanding SAT Mathematics Scores with the Empirical RuleThe mean mathematics SAT score for all people who took the SAT in a particular year was 514 with a standard deviation of 117. Assume the mathematics SAT score is normally distributed.#### a) Identifying Components:**Individual, Variable, and Type of Variable:**- **The individual** is a randomly selected person who took the SAT.- **The variable** collected from each individual is the mathematics SAT score.- **This variable** is a quantitative -- discrete variable.#### b) Definition of Random Variable X:**Random Variable X:**- The random variable X = the mathematics SAT score of a randomly selected person who took the SAT.#### c) Application of Empirical Rule:**Empirical Rule Application:**- The Empirical Rule can only be used to approximate probabilities for problems where the random variable has a normal distribution. Since the mathematics SAT score is normally distributed, the Empirical Rule is applicable here.#### d) Calculating Probabilities using Empirical Rule:**Percentage of People Scoring Between 163 and 631:**- There is about 83.85% of people who take the SAT that will have a mathematics SAT score between 163 and 631.#### e) Percentage of People Scoring At Least 397:**Percentage of People Scoring At Least 397:**- There is about 34% of people who take the SAT that will have a mathematics SAT score of at least 397. Note that this part contained a mistake as the correct percentage should be analyzed and corrected according to the accurate use of the Empirical Rule.*Note: The Empirical Rule states that approximately 68% of data within one standard deviation (±1σ), 95% within two (±2σ), and 99.7% within three (±3σ).*---This exercise demonstrates the proper use of statistical tools and methods for analyzing normally distributed data, essential in various educational assessments and research.

It is given that Mean, μ = 514Standard deviation, σ = 117

e) Use the Empirical Rule to approximate the percentage of people who take the SAT that will I have a mathematics SAT score of at least 397? • There is about 34 score of a least 397. X% of people who take the SAT that will have a mathematics SAT

e) Use the Empirical Rule to approximate the percentage of people who take the SAT that will I have a mathematics SAT score of at least 397? • There is about 34 score of a least 397. X% of people who take the SAT that will have a mathematics SAT

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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Question

E)Use the empirical rule to approximate the percentage of people who take the SAT that will have a mathematics SAT score at least 397.

---
### Understanding SAT Mathematics Scores with the Empirical Rule

The mean mathematics SAT score for all people who took the SAT in a particular year was 514 with a standard deviation of 117. Assume the mathematics SAT score is normally distributed.

#### a) Identifying Components:
**Individual, Variable, and Type of Variable:**
- **The individual** is a randomly selected person who took the SAT.
- **The variable** collected from each individual is the mathematics SAT score.
- **This variable** is a quantitative -- discrete variable.

#### b) Definition of Random Variable X:
**Random Variable X:**
- The random variable X = the mathematics SAT score of a randomly selected person who took the SAT.

#### c) Application of Empirical Rule:
**Empirical Rule Application:**
- The Empirical Rule can only be used to approximate probabilities for problems where the random variable has a normal distribution. Since the mathematics SAT score is normally distributed, the Empirical Rule is applicable here.

#### d) Calculating Probabilities using Empirical Rule:
**Percentage of People Scoring Between 163 and 631:**
- There is about 83.85% of people who take the SAT that will have a mathematics SAT score between 163 and 631.

#### e) Percentage of People Scoring At Least 397:
**Percentage of People Scoring At Least 397:**
- There is about 34% of people who take the SAT that will have a mathematics SAT score of at least 397. Note that this part contained a mistake as the correct percentage should be analyzed and corrected according to the accurate use of the Empirical Rule.

*Note: The Empirical Rule states that approximately 68% of data within one standard deviation (±1σ), 95% within two (±2σ), and 99.7% within three (±3σ).*

---

This exercise demonstrates the proper use of statistical tools and methods for analyzing normally distributed data, essential in various educational assessments and research.

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