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Is is unusual for someone to run a 4 minute mile if the mean time is 10.2 minutes and the standard deviation is 2.9 minutes? yes (yes/no) because the z score is 2.14

Is is unusual for someone to run a 4 minute mile if the mean time is 10.2 minutes and the standard deviation is 2.9 minutes? yes (yes/no) because the z score is 2.14

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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### Statistical Analysis Example #### Problem: Is it unusual for someone to run a 4-minute mile if the mean time is 10.2 minutes and the standard deviation is 2.9 minutes? #### Solution: **Answer:** - **Yes** (Yes/No) because the z-score is **2.14**. The z-score is calculated using the formula: \[ z = \frac{X - \mu}{\sigma} \] where: - \( X \) = 4 minutes (time to run a mile) - \( \mu \) = 10.2 minutes (mean time) - \( \sigma \) = 2.9 minutes (standard deviation) ### Explanation: A z-score of 2.14 means that the 4-minute mile is 2.14 standard deviations below the mean time of 10.2 minutes. In the context of a normal distribution, a z-score greater than 2 (in magnitude) is generally considered to indicate that the value is unusual. ### Diagram: Unfortunately, the image does not contain any graphs or diagrams. However, a typical illustration to accompany this information would be a bell curve (normal distribution curve) showing the mean at the highest point and the z-score positioned on the curve to indicate its distance from the mean.
Transcribed Image Text:### Statistical Analysis Example #### Problem: Is it unusual for someone to run a 4-minute mile if the mean time is 10.2 minutes and the standard deviation is 2.9 minutes? #### Solution: **Answer:** - **Yes** (Yes/No) because the z-score is **2.14**. The z-score is calculated using the formula: \[ z = \frac{X - \mu}{\sigma} \] where: - \( X \) = 4 minutes (time to run a mile) - \( \mu \) = 10.2 minutes (mean time) - \( \sigma \) = 2.9 minutes (standard deviation) ### Explanation: A z-score of 2.14 means that the 4-minute mile is 2.14 standard deviations below the mean time of 10.2 minutes. In the context of a normal distribution, a z-score greater than 2 (in magnitude) is generally considered to indicate that the value is unusual. ### Diagram: Unfortunately, the image does not contain any graphs or diagrams. However, a typical illustration to accompany this information would be a bell curve (normal distribution curve) showing the mean at the highest point and the z-score positioned on the curve to indicate its distance from the mean.
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