Evaluate $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$ if $\bar{x}=85.1, \mu=28.2, \sigma=8.6$, and $n=58$ \[ z= \] (Type an integer or decimal rounded to two decimal places as needed.)

Step 1 ：We are given the mean (\(\mu\)) as 28.2, the standard deviation (\(\sigma\)) as 8.6, the sample mean (\(\bar{x}\)) as 85.1, and the sample size (\(n\)) as 58.

Step 2 ：We are asked to calculate the z-score, which measures how many standard deviations an element is from the mean. The formula for the z-score is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).

Step 3 ：Substitute the given values into the formula: \(z=\frac{85.1-28.2}{\frac{8.6}{\sqrt{58}}}\).

Step 4 ：Solving the above expression gives us the z-score as approximately 50.39.

Step 5 ：Final Answer: The z-score is \(\boxed{50.39}\).