Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of -0.9 (to 2 decimal places)

To find the height corresponding to a z-score of \(-0.9\), we use the z-score formula:

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

Where:
- \( z \) is the z-score (\(-0.9\)),
- \( X \) is the height we are solving for,
- \( \mu \) is the mean height (\(69.0\) inches),
- \( \sigma \) is the standard deviation (\(2.8\) inches).

Rearranging the formula to solve for \( X \):

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

Substitute the given values:

\[
X = (-0.9) \cdot 2.8 + 69.0
\]

Now, let's compute the value:

\[
X = -2.52 + 69.0 = 66.48 \, \text{inches}
\]

So, the height of the man with a z-score of \(-0.9\) is \( \mathbf{66.48} \) inches.

Would you like further details or have any other questions?

Here are 5 related questions:
1. What does a positive z-score indicate in this context?
2. How would you interpret a z-score of \(0\)?
3. If a man has a height of 71.8 inches, what is his z-score?
4. What proportion of men have heights below 66.48 inches?
5. How would the z-score change if the standard deviation increased?

**Tip:** The z-score helps you understand how far a value is from the mean in terms of standard deviations.

Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of -0.9 (to 2 decimal places).

Learn how to calculate the height of a man given a z-score of -0.9, using a mean height of 69.0 inches and a standard deviation of 2.8 inches. This problem demonstrates the application of the z-score formula in a normal distribution. Suitable for high school students in Grades 10-12.

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