Use z scores to compare the given values. The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme? ….. Since the z score for the tallest man is z = and the z score for the shortest man is z = the man had the height that was Im- more extreme. (Round to two decimal places.) shortest tallest
Use z scores to compare the given values. The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme? ….. Since the z score for the tallest man is z = and the z score for the shortest man is z = the man had the height that was Im- more extreme. (Round to two decimal places.) shortest tallest
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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![### Comparing Heights Using Z-Scores
To compare the given values using z-scores:
#### Problem Statement
The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme?
To answer this question, we can calculate the z-scores for both heights.
#### Calculation
The z-score formula is:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( X \) is the value (height in this case) we are evaluating,
- \( \mu \) is the mean height,
- \( \sigma \) is the standard deviation of the height.
For the tallest man:
- \( X = 238 \)
- \( \mu = 175.45 \)
- \( \sigma = 5.59 \)
Plugging in the values:
\[ z_{tallest} = \frac{(238 - 175.45)}{5.59} \]
For the shortest man:
- \( X = 142.4 \)
- \( \mu = 175.45 \)
- \( \sigma = 5.59 \)
Plugging in the values:
\[ z_{shortest} = \frac{(142.4 - 175.45)}{5.59} \]
#### Determination of Extremity
After calculating the z-scores for both the tallest and the shortest man, we can compare their absolute values to determine which height is more extreme.
The man with the larger absolute z-score has the more extreme value.
#### Interactive Part
Since the z score for the tallest man is \( z = \_\_\_ \) and the z score for the shortest man is \( z = \_\_\_ \), the \_\_\_\_\_ man had the height that was more extreme. (Round to two decimal places.)
Insert the appropriate values and select either "shortest" or "tallest" from the dropdown menu.
#### Visualization
*No specific graphs or diagrams are provided in the original image for further explanation.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cbada35-3122-4a6c-a25c-246bca0ae236%2Fd67e5b9e-4963-4e4a-b4ee-edee04203e98%2F52cxivw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Comparing Heights Using Z-Scores
To compare the given values using z-scores:
#### Problem Statement
The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme?
To answer this question, we can calculate the z-scores for both heights.
#### Calculation
The z-score formula is:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( X \) is the value (height in this case) we are evaluating,
- \( \mu \) is the mean height,
- \( \sigma \) is the standard deviation of the height.
For the tallest man:
- \( X = 238 \)
- \( \mu = 175.45 \)
- \( \sigma = 5.59 \)
Plugging in the values:
\[ z_{tallest} = \frac{(238 - 175.45)}{5.59} \]
For the shortest man:
- \( X = 142.4 \)
- \( \mu = 175.45 \)
- \( \sigma = 5.59 \)
Plugging in the values:
\[ z_{shortest} = \frac{(142.4 - 175.45)}{5.59} \]
#### Determination of Extremity
After calculating the z-scores for both the tallest and the shortest man, we can compare their absolute values to determine which height is more extreme.
The man with the larger absolute z-score has the more extreme value.
#### Interactive Part
Since the z score for the tallest man is \( z = \_\_\_ \) and the z score for the shortest man is \( z = \_\_\_ \), the \_\_\_\_\_ man had the height that was more extreme. (Round to two decimal places.)
Insert the appropriate values and select either "shortest" or "tallest" from the dropdown menu.
#### Visualization
*No specific graphs or diagrams are provided in the original image for further explanation.*
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