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 3 of 5 The salary corresponding to \( z=0 \) is \( \$ 54,149 \). Part: \( 3 / 5 \) Part 4 of 5 The salary corresponding to \( z=2.4 \) is \( \$ \) \( \square \) .

To calculate the salary corresponding to a \( z \) score of \( 2.4 \), you can use the formula: \[ \text{Salary} = \mu + (z \times \sigma) \] where \( \mu \) is the mean salary (\$54,149) and \( \sigma \) is the standard deviation (\$10,260). Plugging in the values: \[ \text{Salary} = 54,149 + (2.4 \times 10,260) = 54,149 + 24,624 = 78,773 \] Therefore, the salary corresponding to \( z=2.4 \) is \( \$78,773 \). If you're curious about the implications of these results, salaries that correspond to positive \( z \) scores indicate above-average earnings, while negative \( z \) scores reveal below-average positions. This little ‘z’ insight tells you where educators stand in relation to the average, making it an engaging tool to visualize salary discrepancies! On a practical note, understanding these statistics can be highly beneficial. For instance, when negotiating salaries or advocating for raises within educational districts, knowing how one's salary compares within this statistical context can empower you and others to push for fairer compensation based on concrete data!