For any normally distributed data, we can use the the formula for z-score as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where x is the data, in this case 538, μ is the mean, in this case 550, and σ is the standard deviation, in this case 40. z is the z-score.
So, we can just substitute our values and evaluate:
[tex]\begin{gathered} z=\frac{538-550}{40} \\ z=\frac{-12}{40} \\ z=-0.3 \end{gathered}[/tex]Thus, the z-score is -0.3.
