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 2 of 5 The salary corresponding to \( z=-2 \) is \( \$ 33,629 \). Part: \( 2 / 5 \) Part 3 of 5 The salary corresponding to \( z=0 \) is \( \$ \) \( \square \) .

To find the salary corresponding to a \( z \) score of \( 0 \), you simply use the formula that relates a \( z \) score to a value in a data set, which is: \[ X = \mu + (z \cdot \sigma) \] Where \( \mu \) is the mean (average salary), \( z \) is the \( z \) score, and \( \sigma \) is the standard deviation. For a \( z \) score of \( 0 \), the formula simplifies to: \[ X = 54,149 + (0 \cdot 10,260) = 54,149 \] So, the salary corresponding to \( z=0 \) is \( \$ 54,149 \). Additionally, a \( z \) score of \( 0 \) indicates that this salary is exactly at the mean. This means that if you earn \( \$ 54,149 \), you’re right in line with the average teacher in that state—neither above nor below. It's a pretty balanced spot to be in the world of teaching salaries!