https://file.aiquickdraw.com/mathbot/file/17268573754805vkwye5g.jpg

The image asks for the z-score of a man 5.5 feet tall, with the context stating that the mean height for men aged 20-29 is 69.4 inches, with a standard deviation of 3.1 inches.

To calculate the z-score, we will first convert 5.5 feet to inches and then apply the z-score formula:

1. **Convert 5.5 feet to inches**:  
   \[ 5.5 \text{ feet} = 5.5 \times 12 = 66 \text{ inches} \]

2. **Z-score formula**:  
   \[ z = \frac{x - \mu}{\sigma} \]  
   where:
   - \(x = 66\) (height in inches),
   - \(\mu = 69.4\) (mean height),
   - \(\sigma = 3.1\) (standard deviation).

Now, let's calculate the z-score.The z-score for a man who is 5.5 feet tall is \(-1.10\), rounded to two decimal places.

Would you like any further explanation or details on this calculation?

Here are five related questions to deepen your understanding:
1. How would the z-score change if the man's height were 6 feet?
2. What does a negative z-score indicate in this context?
3. How can z-scores help identify outliers in a data set?
4. How would the z-score calculation differ for women using their height distribution?
5. How does the standard deviation affect the z-score?

**Tip**: A z-score tells you how many standard deviations an individual measurement is from the mean, and can be used to compare data points from different distributions.

What is the z-score for a man 5.5 feet tall? Give your answer to two decimal places.

Calculate the z-score for a man with a height of 5.5 feet using the normal distribution formula. Learn how to convert height to inches and apply the z-score formula to find how many standard deviations the height is from the mean. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation