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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

Problem 1P

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Question

**Race Performance Analysis**

Robert finished a triathlon in 64.5 minutes. Among all men in the race, the mean finish time was 69.4 minutes with a standard deviation of 8.9 minutes. Michelle ran the same triathlon and finished in 79.3 minutes. Among all women in the race, the mean finish time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better, relative to their gender? *Use the box to justify your choice/show your work.*

O Robert
O Michelle

**Explanation:**

The problem asks us to compare the performance of Robert and Michelle relative to their respective gender groups by using the concept of standard deviation.

Robert's time: 64.5 minutes
Men's mean time: 69.4 minutes
Men's standard deviation: 8.9 minutes

Michelle's time: 79.3 minutes
Women's mean time: 84.7 minutes
Women's standard deviation: 7.4 minutes

To determine who performed better relative to their gender group, we calculate how many standard deviations each time is from the mean. This can be done using the Z-score formula:

\[ Z = \frac{{X - \mu}}{\sigma} \]

Where:
- \( X \) is the individual's finish time
- \( \mu \) is the mean finish time
- \( \sigma \) is the standard deviation

Calculate the Z-score for Robert and Michelle to see who performed better compared to their peers.

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