**Calculating Z-Scores for ERA in Baseball**In one particular year, Sam achieved the lowest ERA (earned-run average, the mean number of runs yielded per nine innings pitched) among male pitchers at his school, with an ERA of 3.05. Nina, similarly, had the lowest ERA among female pitchers at her school, with an ERA of 3.34. ### Statistical Comparison:- **Males:** - Mean ERA: 4.705 - Standard Deviation: 0.852- **Females:** - Mean ERA: 4.554 - Standard Deviation: 0.501### Task: Calculate and Compare Z-ScoresCalculate the Z-scores for both Sam and Nina to determine who performed better relative to their peers. The formula for calculating a Z-score is:\[ Z = \frac{(X - \text{Mean})}{\text{Standard Deviation}} \]**Sam's Z-score**\[ Z = \frac{(3.05 - 4.705)}{0.852} \]**Nina's Z-score**\[ Z = \frac{(3.34 - 4.554)}{0.501} \]### Determine the Better Performance:A lower ERA generally indicates better performance for a pitcher, and a lower Z-score represents a performance further below the mean of the group.**Note:** For accuracy, round your calculations to two decimal places. **Exercise:**Fill in the blanks with the calculated Z-scores:- Sam had an ERA with a Z-score of ______- Nina had an ERA with a Z-score of ______Evaluate who had the better relative performance based on their Z-scores.

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Description: **Calculating Z-Scores for ERA in Baseball**In one particular year, Sam achieved the lowest ERA (earned-run average, the mean number of runs yielded per nine innings pitched) among male pitchers at his school, with an ERA of 3.05. Nina, similarly, h

From the provided information, The mean and standard deviation for the males ERA are as follow: Mean…

Math

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One year Sam had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.05. Also, Nina had the lowest ERA of any female pitcher at the school with an ERA of 3.34. For the males, the mean ERA was 4.705 and the standard deviation was 0.852. For the females, the mean ERA was 4.554 and the standard deviation was 0.501. Find their respective Z-scores. Which player had the better year relative to their peers, Sam or Nina? (Note: In general, the lower the ERA, the better the pitcher.) Sam had an ERA with a z-score of Nina had an ERA with a z-score of (Round to two decimal places as needed.)

One year Sam had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.05. Also, Nina had the lowest ERA of any female pitcher at the school with an ERA of 3.34. For the males, the mean ERA was 4.705 and the standard deviation was 0.852. For the females, the mean ERA was 4.554 and the standard deviation was 0.501. Find their respective Z-scores. Which player had the better year relative to their peers, Sam or Nina? (Note: In general, the lower the ERA, the better the pitcher.) Sam had an ERA with a z-score of Nina had an ERA with a z-score of (Round to two decimal places as needed.)

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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