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Which score indicates the highest relative position? Round your answer to two decimal places, if necessary. (a) A score of 3.4 on a test with X=4.2 and s= 1.6. - (b) A score of 640 on a test with X= 780 and s=240. (c) A score of 43 on a test with X=49 and s=3. The score with the highest relative position is (Choose one) ▼ since the (Choose one) X is highest.

Which score indicates the highest relative position? Round your answer to two decimal places, if necessary. (a) A score of 3.4 on a test with X=4.2 and s= 1.6. - (b) A score of 640 on a test with X= 780 and s=240. (c) A score of 43 on a test with X=49 and s=3. The score with the highest relative position is (Choose one) ▼ since the (Choose one) X is highest.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Problem Statement: Which score indicates the highest relative position? Round your answer to two decimal places, if necessary. (a) A score of 3.4 on a test with \( \overline{X} = 4.2 \) and \( s = 1.6 \). (b) A score of 640 on a test with \( \overline{X} = 780 \) and \( s = 240 \). (c) A score of 43 on a test with \( \overline{X} = 49 \) and \( s = 3 \). ### Solution: To find the highest relative position, calculate the z-score for each option using the formula: \[ z = \frac{X - \overline{X}}{s} \] 1. **Option (a):** \[ z = \frac{3.4 - 4.2}{1.6} = \frac{-0.8}{1.6} = -0.50 \] 2. **Option (b):** \[ z = \frac{640 - 780}{240} = \frac{-140}{240} = -0.58 \] 3. **Option (c):** \[ z = \frac{43 - 49}{3} = \frac{-6}{3} = -2.00 \] ### Interpretation: The score with the highest relative position is (a) since the z-score of -0.50 is the highest. ### Interactive Element: The dropdown options for filling in the blanks would be: - For "The score with the highest relative position is": - Choose one: (a), (b), (c) - For "since the (Choose one) is highest": - Choose one: z-score, relative position ### Conclusion: Based on the calculations, option (a) is the correct answer because it has the highest z-score of -0.50, indicating it is closest to the mean compared to the other options.
Transcribed Image Text:### Problem Statement: Which score indicates the highest relative position? Round your answer to two decimal places, if necessary. (a) A score of 3.4 on a test with \( \overline{X} = 4.2 \) and \( s = 1.6 \). (b) A score of 640 on a test with \( \overline{X} = 780 \) and \( s = 240 \). (c) A score of 43 on a test with \( \overline{X} = 49 \) and \( s = 3 \). ### Solution: To find the highest relative position, calculate the z-score for each option using the formula: \[ z = \frac{X - \overline{X}}{s} \] 1. **Option (a):** \[ z = \frac{3.4 - 4.2}{1.6} = \frac{-0.8}{1.6} = -0.50 \] 2. **Option (b):** \[ z = \frac{640 - 780}{240} = \frac{-140}{240} = -0.58 \] 3. **Option (c):** \[ z = \frac{43 - 49}{3} = \frac{-6}{3} = -2.00 \] ### Interpretation: The score with the highest relative position is (a) since the z-score of -0.50 is the highest. ### Interactive Element: The dropdown options for filling in the blanks would be: - For "The score with the highest relative position is": - Choose one: (a), (b), (c) - For "since the (Choose one) is highest": - Choose one: z-score, relative position ### Conclusion: Based on the calculations, option (a) is the correct answer because it has the highest z-score of -0.50, indicating it is closest to the mean compared to the other options.
Expert Solution
Step 1: Expplain the basic information.

The question is about z score.

Introduction :

1 ) The formula of z score is given by

z space equals space fraction numerator x space minus space X with bar on top over denominator s end fraction

2 ) z score is always unitless.

3 ) z scores are used to identify the outliers.

4 ) It is also known as standard score.


To find :

Which score indicates highest relative position?


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