following: a) The percent of students that scored over 575. b) The number of students that scored less than 425. c) The probability of a student selected at random having scored between 400 and 510.
following: a) The percent of students that scored over 575. b) The number of students that scored less than 425. c) The probability of a student selected at random having scored between 400 and 510.
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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![**Educational Website Content**
### Aptitude Test Analysis for Local High School
Recently, 5000 juniors and seniors at a local high school participated in an aptitude test. The scores from this exam were normally distributed with a mean (μ) of 450 and a standard deviation (σ) of 50. We are tasked with calculating the following:
a) **The percent of students that scored over 575.**
b) **The number of students that scored less than 425.**
c) **The probability of a student selected at random having scored between 400 and 510.**
*Note: The calculations will involve using properties of the normal distribution and may require the use of Z-scores and standard normal distribution tables.*
---
### Explanation of Calculations
- **Normal Distribution**: This is a probability distribution that is symmetric around the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
- **Z-Score**: This is a measure of how many standard deviations an element is from the mean. The formula to calculate the Z-score is:
\[
Z = \frac{(X - \mu)}{\sigma}
\]
where \(X\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
- **Standard Normal Distribution Table**: This table is used to find probabilities associated with the Z-scores.
Each calculation involves determining the Z-score for the score in question and then using the standard normal distribution to find the corresponding probability or percentage.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5192e005-256c-41a3-b518-ed0a7cd5622c%2Fbe4b86e0-9c9d-42af-94c1-73a44e446964%2Fwa7lhz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
### Aptitude Test Analysis for Local High School
Recently, 5000 juniors and seniors at a local high school participated in an aptitude test. The scores from this exam were normally distributed with a mean (μ) of 450 and a standard deviation (σ) of 50. We are tasked with calculating the following:
a) **The percent of students that scored over 575.**
b) **The number of students that scored less than 425.**
c) **The probability of a student selected at random having scored between 400 and 510.**
*Note: The calculations will involve using properties of the normal distribution and may require the use of Z-scores and standard normal distribution tables.*
---
### Explanation of Calculations
- **Normal Distribution**: This is a probability distribution that is symmetric around the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
- **Z-Score**: This is a measure of how many standard deviations an element is from the mean. The formula to calculate the Z-score is:
\[
Z = \frac{(X - \mu)}{\sigma}
\]
where \(X\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
- **Standard Normal Distribution Table**: This table is used to find probabilities associated with the Z-scores.
Each calculation involves determining the Z-score for the score in question and then using the standard normal distribution to find the corresponding probability or percentage.
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