https://file.aiquickdraw.com/mathbot/file/1728080651983ri1lzaf0.jpg

The problem involves calculating the z-score for a given height using the formula:

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

Where:
- \(x\) is the value (height of the man = 69.8 inches),
- \(\mu\) is the mean (69.0 inches),
- \(\sigma\) is the standard deviation (2.8 inches).

Now we can plug in the values:

\[
z = \frac{69.8 - 69.0}{2.8} = \frac{0.8}{2.8} \approx 0.2857
\]

Thus, the z-score of a man who is 69.8 inches tall is approximately **0.2857**.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this:
1. What does a z-score represent in statistical terms?
2. How would you interpret a negative z-score?
3. Can the z-score formula be applied to other data types?
4. What is the probability associated with a z-score of 0.2857?
5. How does standard deviation impact the z-score?

**Tip:** A z-score tells you how many standard deviations a value is from the mean. Values above the mean have positive z-scores, and values below the mean have negative z-scores.

Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man who is 69.8 inches tall. (to 4 decimal places)

Learn how to calculate the z-score for a man who is 69.8 inches tall, given a population mean height of 69.0 inches and a standard deviation of 2.8 inches. This problem demonstrates the use of the z-score formula in statistics and is suitable for students in Grades 9-12.

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