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)
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)
Solution
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