**Case Study: Comparing Performance Using Z-Scores**Two friends, Virgil and Mohammad, have decided to take a welding class together. Here's a breakdown of their performance on quizzes:- **Virgil's Score Summary:** - First Quiz: Virgil scored 38. - Class average: 42 - Standard deviation: 5- **Mohammad's Score Summary:** - Second Quiz: Mohammad scored 40. - Class average: 45 - Standard deviation: 6.1### Analysis:**Objective:** Determine if Mohammad really performed better than Virgil based on their quiz scores using z-scores for comparison.**Definitions:**- **Z-Score Formula:** \[ Z = \frac{(X - \text{Mean})}{\text{Standard Deviation}} \]- **Calculation:** - **Virgil’s Z-Score:** \[ Z_{\text{Virgil}} = \frac{38 - 42}{5} = \frac{-4}{5} = -0.8 \] - **Mohammad’s Z-Score:** \[ Z_{\text{Mohammad}} = \frac{40 - 45}{6.1} = \frac{-5}{6.1} \approx -0.82 \]### Conclusion:Based on the z-scores:- **Z-Mohammad ≈ -0.82** is slightly more negative than **Z-Virgil = -0.8.**Therefore, Mohammad did not perform better than Virgil when comparing their performances relative to their respective class averages and standard deviations.#### Options to Consider:- **Yes. \(Z_{\text{Mohammad}}\) is more negative than \(Z_{\text{Virgil}}\).**- **Yes. \(Z_{\text{Mohammad}}\) is less negative than \(Z_{\text{Virgil}}\).**- **No. \(Z_{\text{Mohammad}}\) is less negative than \(Z_{\text{Virgil}}\).**- **No. \(Z_{\text{Mohammad}}\) is more negative than \(Z_{\text{Virgil}}\).****Correct Evaluation:**- The correct choice is: - **No. \(Z_{\text{Mohammad}}\) is more negative than \(Z_{\text{Virgil

Two friends have decided to take a Welding class together. Virgil got 38 on the first quiz of the semester. The class average on the first quiz was 42 with a standard deviation of 5. Mohammad, who was absent when the first quiz was given, got 40 on the second quiz. The class average on the second quiz was 45 with a standard deviation of 6.1. Virgil was absent for the second quiz. After the second quiz, Mohammad told Virgil that he was doing better in class because they had each taken one quiz, and he had earned the higher score. Did Mohammad really perform better than Virgil?

Two friends have decided to take a Welding class together. Virgil got 38 on the first quiz of the semester. The class average on the first quiz was 42 with a standard deviation of 5. Mohammad, who was absent when the first quiz was given, got 40 on the second quiz. The class average on the second quiz was 45 with a standard deviation of 6.1. Virgil was absent for the second quiz. After the second quiz, Mohammad told Virgil that he was doing better in class because they had each taken one quiz, and he had earned the higher score. Did Mohammad really perform better than Virgil?

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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