Questions: 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 -1.9 (to 2 decimal places)

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 -1.9 (to 2 decimal places)
Transcript text: 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 -1.9 (to 2 decimal places)
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Solution

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Solution Steps

Step 1: Given Information

We are provided with the following parameters for the heights of adult men:

  • Mean height (\( \mu \)): 69.0 inches
  • Standard deviation (\( \sigma \)): 2.8 inches
  • \( z \)-score: -1.9
Step 2: Calculate the Height

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

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

Substituting the known values:

\[ x = 69.0 + (-1.9) \cdot 2.8 \]

Calculating the product:

\[ (-1.9) \cdot 2.8 = -5.32 \]

Now substituting back into the equation:

\[ x = 69.0 - 5.32 = 63.68 \]

Final Answer

The height of a man with a \( z \)-score of -1.9 is

\[ \boxed{x = 63.68 \text{ inches}} \]

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