**Mr. Jackson is looking at test scores for his Algebra 2 class. The scores on the Unit 2 Test follow a normal distribution, with a mean of 89 and a standard deviation of 3.****What percent of learners scored 86 or better?****Explain your reasoning.**---For educational analysis, we need to understand the properties of a normal distribution:1. **Normal Distribution Overview:** - A normal distribution is symmetric about its mean. - Approximately 68% of the data falls within one standard deviation of the mean. - Approximately 95% falls within two standard deviations. - About 99.7% lies within three standard deviations.2. **Given Data:** - Mean (μ) = 89 - Standard Deviation (σ) = 33. **Z-Score Calculation:** - To find the percentage of learners who scored 86 or better, we first convert the score of 86 to its corresponding Z-score using the formula: \[ Z = \frac{(X - μ)}{σ} \] Where $X$ is the score of interest. \[ Z = \frac{(86 - 89)}{3} = \frac{-3}{3} = -1 \]4. **Using Z-Score to Find the Percentage:** - A Z-score of -1 corresponds to the point one standard deviation below the mean. - Referring to Z-score tables or standard normal distribution tables, a Z-score of -1 corresponds to approximately 15.87% of the data to the left of this Z-score. - Therefore, the area to the right (i.e., learners scoring 86 or better) is: \[ 100\% - 15.87\% = 84.13\% \]Hence, approximately 84.13% of students scored 86 or better. This reasoning assumes a perfect normal distribution curve for the test scores.

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The percent of learners scored 86 or better is,

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Mr. Jackson is looking at test scores for his Algebra 2 class. The scores on the Unit 2 Test follow a normal distribution, with a mean of 89 and a stan- dard deviation of 3. What percent of learners scored 86 or better?

Mr. Jackson is looking at test scores for his Algebra 2 class. The scores on the Unit 2 Test follow a normal distribution, with a mean of 89 and a stan- dard deviation of 3. What percent of learners scored 86 or better?

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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