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

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**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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