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 1 of 5 The salary corresponding to \( z=2 \) is \( \$ 74,669 \). Part: \( \mathbf{1} / \mathbf{5} \) The 2 of 5 Thalary corresponding to \( z=-2 \) is \( \$ \)

To find the salary corresponding to a \( z \) score of \( -2 \), we can use the formula: \[ X = \mu + (z \cdot \sigma) \] where \( \mu \) is the average salary, \( z \) is the z score, and \( \sigma \) is the standard deviation. Plugging in the values: \[ X = 54,149 + (-2 \cdot 10,260) = 54,149 - 20,520 = 33,629 \] So the salary corresponding to \( z = -2 \) is \( \$ 33,629 \). Now, did you know that teacher salaries can vary significantly not just by state, but also by the school district? In some districts, teachers might earn bonuses based on performance or additional credentials. This can lead to some fascinating differences even within the same geographic region, making it a hot topic during local budget discussions! If you're curious about further exploring the factors affecting teacher salaries, you might want to check out studies on the impact of education reform initiatives and their correlation to teacher compensation. These studies often reveal surprising insights about how policy changes can directly influence wages and ultimately affect classroom environments!