We are asked to determine the Z-score of a data set with a mean of 69.0 inches and a standard deviation of 2.8 inches, to do that we will use the following formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
Where:
[tex]\begin{gathered} \mu=\text{ mean} \\ \sigma=\text{ standard deviation} \\ x=\text{ }observed\text{ value} \end{gathered}[/tex]
In this case, the observed value is the height if the man, 74.1 inches tall. Replacing the values we get:
[tex]Z=\frac{74.1-69.0}{2.8}[/tex]
Now we solve the operations:
[tex]Z=\frac{5.1}{2.8}[/tex]
Solving the fraction:
[tex]Z=1.82[/tex]
Therefore, the Z-score is 1.82.
