The heights of adult men in America are normally distributed, with a mean of 69.7 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, with a mean of 64.7 inches and a standard deviation of 2.56 inches. Keep in mind that if someone is 6 foot and 5 inches tall then their height would be equivalent to 6 x 12 + 5 = 77 inches a. If a man is 6 feet and 3 inches tall, what is his z-score? (Round to two decimal places) = Z b. If a woman is 5 feet and 11 inches tall, what is her z-score? (Round to two decimal places) c. Who is relatively taller? O The man at 6 foot and 3 inches tall O The woman at 5 foot and 11 inches tall 93 F Sunny e to search
The heights of adult men in America are normally distributed, with a mean of 69.7 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, with a mean of 64.7 inches and a standard deviation of 2.56 inches. Keep in mind that if someone is 6 foot and 5 inches tall then their height would be equivalent to 6 x 12 + 5 = 77 inches a. If a man is 6 feet and 3 inches tall, what is his z-score? (Round to two decimal places) = Z b. If a woman is 5 feet and 11 inches tall, what is her z-score? (Round to two decimal places) c. Who is relatively taller? O The man at 6 foot and 3 inches tall O The woman at 5 foot and 11 inches tall 93 F Sunny e to search
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Understanding Z-Scores in Relation to Height**
This educational section aims to help you understand how to calculate and interpret z-scores through the example of heights among American adults.
**The heights of adult men in America are normally distributed**, with a mean (average) height of 69.7 inches and a standard deviation of 2.69 inches. On the other hand, **the heights of adult women in America are also normally distributed**, with a mean height of 64.7 inches and a standard deviation of 2.56 inches.
*Conversion Tip:* Remember that if someone's height is described in feet and inches, you can convert it to inches for easier calculations. For example, a person who is 6 feet 5 inches tall has a height of \(6 \times 12 + 5 = 77\) inches.
Here's a set of problems to help you apply these concepts:
### Problem Set:
**a. If a man is 6 feet and 3 inches tall, what is his z-score?**
(Round to two decimal places)
\[ z = \]
**b. If a woman is 5 feet and 11 inches tall, what is her z-score?**
(Round to two decimal places)
\[ z = \]
**c. Who is relatively taller?**
- The man at 6 feet and 3 inches tall
- The woman at 5 feet and 11 inches tall
**Explanation of Z-Score Calculation:**
The z-score is calculated as follows:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \(X\) is the value (height in this case),
- \(\mu\) is the mean,
- \(\sigma\) is the standard deviation.
**Diagrams and Graphs:**
While there are no graphs or diagrams provided in this set of exercises, imagine a standard normal distribution curve where the mean height (either 69.7 inches for men or 64.7 inches for women) is at the center. Each z-score represents how many standard deviations away from the mean a particular height is. A positive z-score indicates a height above the mean, while a negative z-score indicates a height below the mean.
Working through these problems will help you better understand and interpret z-scores in real-world contexts, such as comparing individual heights to average values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc9a01fb-7b2f-4b99-a4be-e5812986e7e1%2F03f272c9-d68a-4b66-9cf7-933fb6271743%2Fa5a8oo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Z-Scores in Relation to Height**
This educational section aims to help you understand how to calculate and interpret z-scores through the example of heights among American adults.
**The heights of adult men in America are normally distributed**, with a mean (average) height of 69.7 inches and a standard deviation of 2.69 inches. On the other hand, **the heights of adult women in America are also normally distributed**, with a mean height of 64.7 inches and a standard deviation of 2.56 inches.
*Conversion Tip:* Remember that if someone's height is described in feet and inches, you can convert it to inches for easier calculations. For example, a person who is 6 feet 5 inches tall has a height of \(6 \times 12 + 5 = 77\) inches.
Here's a set of problems to help you apply these concepts:
### Problem Set:
**a. If a man is 6 feet and 3 inches tall, what is his z-score?**
(Round to two decimal places)
\[ z = \]
**b. If a woman is 5 feet and 11 inches tall, what is her z-score?**
(Round to two decimal places)
\[ z = \]
**c. Who is relatively taller?**
- The man at 6 feet and 3 inches tall
- The woman at 5 feet and 11 inches tall
**Explanation of Z-Score Calculation:**
The z-score is calculated as follows:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \(X\) is the value (height in this case),
- \(\mu\) is the mean,
- \(\sigma\) is the standard deviation.
**Diagrams and Graphs:**
While there are no graphs or diagrams provided in this set of exercises, imagine a standard normal distribution curve where the mean height (either 69.7 inches for men or 64.7 inches for women) is at the center. Each z-score represents how many standard deviations away from the mean a particular height is. A positive z-score indicates a height above the mean, while a negative z-score indicates a height below the mean.
Working through these problems will help you better understand and interpret z-scores in real-world contexts, such as comparing individual heights to average values.
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