### Standardized Test Scores ComparisonEleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 565 and standard deviation 116.Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.3 and standard deviation 3.7.**a. What is Eleanor's standardized score?**\[ \text{Round to 2 decimal places.}\]**b. What is Gerald's standardized score?**\[ \text{Round to 2 decimal places.}\]**c. Assuming that both tests measure the same kind of ability, who has the higher score?**- O Gerald.- O Eleanor.- O They both did equally well.### ExplanationTo find the standardized scores (also known as z-scores), we use the following formula:\[ z = \frac{X - \mu}{\sigma}\]Where:- $ X $ is the individual’s score- $ \mu $ is the mean score- $ \sigma $ is the standard deviation**Steps to Calculate:**1. **Eleanor's standardized score:** - Eleanor's SAT score $ X = 680 $ - Mean SAT score $ \mu = 565 $ - Standard deviation of SAT score $ \sigma = 116 $ \[ z = \frac{680 - 565}{116} \approx \frac{115}{116} \approx 0.99 \]2. **Gerald's standardized score:** - Gerald's ACT score $ X = 27 $ - Mean ACT score $ \mu = 21.3 $ - Standard deviation of ACT score $ \sigma = 3.7 $ \[ z = \frac{27 - 21.3}{3.7} \approx \frac{5.7}{3.7} \approx 1.54 \]3. **Comparison:** - Compare the z-scores to determine who has the higher score relative to their respective test distributions. Therefore, based on the calculated z-scores, Gerald has the higher standardized score compared to Eleanor.Note: Values are rounded to two decimal places as specified.

A continuous random variable X is said to follow Normal distribution with parameters μ and σ2 if its…

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 565 and standard deviation 116. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.3 and standard deviation 3.7. a. What is Elanor's standardized score? Round to 2 decimal places. b. What is Gerald's standardized score? Round to 2 decimal places. c. Assuming that both tests measure the same kind of ability, who has the higher score? O Gerald. O Elanor. O They both did equally well.

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 565 and standard deviation 116. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.3 and standard deviation 3.7. a. What is Elanor's standardized score? Round to 2 decimal places. b. What is Gerald's standardized score? Round to 2 decimal places. c. Assuming that both tests measure the same kind of ability, who has the higher score? O Gerald. O Elanor. O They both did equally well.

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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