Heights of WOMEN in the U.S. are normally distributed. Recent information shows: Adult women height: µ = 63.8 inches with σ = 2.8 inches. In a group of 150 U.S. women, approximately ________ women should be shorter than 63 inches? **Sample of RCCC Women’s Heights – Spring 2022**This table presents a statistical sample of the heights of women from RCCC (assumed to be a college or organization), collected during the Spring 2022 semester. Presented heights are in inches and the corresponding frequency (number of women) for each height is listed alongside.| **Height (in inches)** | **Frequency** ||-----------------|------------|| 61 | 4 || 62 | 8 || 63 | 7 || 64 | 7 || 65 | 12 || 66 | 3 || 67 | 7 || 68 | 2 || 69 | 0 || 70 | 1 || 71 | 0 || 72 | 1 |### Explanation:- The height range covered in the sample is from 61 inches to 72 inches.- The most frequent height recorded is 65 inches, exhibited by 12 women.- Heights 69 inches and 71 inches have no individuals, indicating no women in the sample were of those heights.- The distribution of heights shows a relatively normal distribution with a peak around 65 inches.- This data can be used to understand the general height distribution among the sample population, aiding in further statistical analysis such as mean, median, mode, and standard deviation calculations.### Note:This table can be useful for educational purposes such as teaching students about data collection, frequency distribution, and basic statistical analysis.

Answered: Heights of WOMEN in the U.S. are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Heights of WOMEN in the U.S. are normally distributed. Recent information shows:

Adult women height: µ = 63.8 inches with σ = 2.8 inches.

In a group of 150 U.S. women, approximately ________ women should be shorter than 63 inches?

**Sample of RCCC Women’s Heights – Spring 2022**

This table presents a statistical sample of the heights of women from RCCC (assumed to be a college or organization), collected during the Spring 2022 semester. Presented heights are in inches and the corresponding frequency (number of women) for each height is listed alongside.

| **Height (in inches)** | **Frequency** |
|-----------------|------------|
| 61 | 4 |
| 62 | 8 |
| 63 | 7 |
| 64 | 7 |
| 65 | 12 |
| 66 | 3 |
| 67 | 7 |
| 68 | 2 |
| 69 | 0 |
| 70 | 1 |
| 71 | 0 |
| 72 | 1 |

### Explanation:

- The height range covered in the sample is from 61 inches to 72 inches.
- The most frequent height recorded is 65 inches, exhibited by 12 women.
- Heights 69 inches and 71 inches have no individuals, indicating no women in the sample were of those heights.
- The distribution of heights shows a relatively normal distribution with a peak around 65 inches.
- This data can be used to understand the general height distribution among the sample population, aiding in further statistical analysis such as mean, median, mode, and standard deviation calculations.

### Note:

This table can be useful for educational purposes such as teaching students about data collection, frequency distribution, and basic statistical analysis.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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