Teacher's Salary The average teacher's salary in a particular state is \( \$ 54,149 \). If the standard deviation is \( \$ 10 \), 260 , find the salaries corresponding to the following \( z \) scores. Part: \( \mathbf{0} / \mathbf{5} \) Part 1 of 5 The salary corresponding to \( z=2 \) is \( \$ \square \)

To find the salary corresponding to \( z = 2 \), we can use the formula for the z-score, which is: \[ z = \frac{(X - \mu)}{\sigma} \] Where: - \( X \) is the value we want to find (the salary), - \( \mu \) is the mean (average teacher's salary), - \( \sigma \) is the standard deviation. Rearranging the formula gives us: \[ X = \mu + z \cdot \sigma \] Substituting in the values: \[ X = 54,149 + 2 \cdot 10 \] Calculating this, we get: \[ X = 54,149 + 20 = 54,169 \] So the salary corresponding to \( z = 2 \) is \( \$ 54,169 \).