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The problem provided asks to find the height of a man with a given z-score, given the average height and standard deviation of adult men.

We can use the formula for the z-score:

\[
z = \frac{X - \mu}{\sigma}
\]

Where:
- \( z \) is the z-score,
- \( X \) is the height we need to find,
- \( \mu = 69.0 \, \text{inches} \) is the average height,
- \( \sigma = 2.8 \, \text{inches} \) is the standard deviation.

Given that the z-score is \( 1.43 \), we solve for \( X \):

\[
X = z \cdot \sigma + \mu
\]

Substituting the values:

\[
X = 1.43 \cdot 2.8 + 69.0
\]

Now, let's calculate this.The height of the man with a z-score of 1.43 is approximately **73.0 inches**, rounded to one decimal place.

Would you like more details or have any further questions?

Here are five related questions for further exploration:
1. What does a z-score represent in a normal distribution?
2. How do you calculate the z-score if you know the height?
3. What does a negative z-score indicate about a person’s height in relation to the average?
4. How would the result change if the standard deviation were different?
5. Why is it important to standardize data using z-scores?

**Tip:** Z-scores allow you to compare values from different datasets by standardizing them, providing a common frame of reference.

Adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. Find the height of a man with a z-score of 1.43. Round your answer to one decimal place.

Learn how to calculate the height of a man using a z-score of 1.43, given an average height of 69.0 inches and a standard deviation of 2.8 inches. This problem involves the application of z-scores and the normal distribution, suitable for Grades 10-12 students.

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