The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.63 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.54 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? Z = 1.98 b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent. 97.6 c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z = 2.56 d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.63 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.54 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? Z = 1.98 b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent. 97.6 c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z = 2.56 d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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part d
![**Understanding Z-Scores and Height Distribution**
In the study of statistics, understanding how data such as heights are distributed can be insightful. Here, we examine the normal distribution of heights for adult men and women in America.
- **Men:** Mean = 69.8 inches, Standard Deviation = 2.63 inches
- **Women:** Mean = 64.5 inches, Standard Deviation = 2.54 inches
### Questions:
**a) If a man is 6 feet 3 inches tall, what is his z-score (rounded to two decimal places)?**
- **Calculation:**
\[ z = \frac{{\text{{Height in inches}} - \text{{Mean}}}}{\text{{Standard Deviation}}} \]
- **Result:**
\[ z = 1.98 \]
**b) What percentage of men are shorter than 6 feet 3 inches? (Rounded to the nearest tenth of a percent.)**
- **Result:**
\[ 97.6\% \]
**c) If a woman is 5 feet 11 inches tall, what is her z-score (rounded to two decimal places)?**
- **Calculation:**
\[ z = \frac{{\text{{Height in inches}} - \text{{Mean}}}}{\text{{Standard Deviation}}} \]
- **Result:**
\[ z = 2.56 \]
**d) What percentage of women are taller than 5 feet 11 inches? (Round to the nearest tenth of a percent.)**
- **Instruction:**
This requires calculating the percentage of women that fall above a certain z-score.
By understanding these calculations, we gain insights into how individual heights compare to the average and the population as a whole.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc24d0110-74e6-4765-afd2-6bfe95475961%2F9ecba5a1-27e7-4d32-a0c4-feb6fb8b6131%2Fbtqj0kf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Z-Scores and Height Distribution**
In the study of statistics, understanding how data such as heights are distributed can be insightful. Here, we examine the normal distribution of heights for adult men and women in America.
- **Men:** Mean = 69.8 inches, Standard Deviation = 2.63 inches
- **Women:** Mean = 64.5 inches, Standard Deviation = 2.54 inches
### Questions:
**a) If a man is 6 feet 3 inches tall, what is his z-score (rounded to two decimal places)?**
- **Calculation:**
\[ z = \frac{{\text{{Height in inches}} - \text{{Mean}}}}{\text{{Standard Deviation}}} \]
- **Result:**
\[ z = 1.98 \]
**b) What percentage of men are shorter than 6 feet 3 inches? (Rounded to the nearest tenth of a percent.)**
- **Result:**
\[ 97.6\% \]
**c) If a woman is 5 feet 11 inches tall, what is her z-score (rounded to two decimal places)?**
- **Calculation:**
\[ z = \frac{{\text{{Height in inches}} - \text{{Mean}}}}{\text{{Standard Deviation}}} \]
- **Result:**
\[ z = 2.56 \]
**d) What percentage of women are taller than 5 feet 11 inches? (Round to the nearest tenth of a percent.)**
- **Instruction:**
This requires calculating the percentage of women that fall above a certain z-score.
By understanding these calculations, we gain insights into how individual heights compare to the average and the population as a whole.
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