The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't?
A) −1.96
B) 1.96
C) 45,100
D) 54,900

Question

Quizplus · Accepted Answer

To find the salary level that divides the teachers into one group that gets a raise and one that doesn't, we need to find the z-score that corresponds to the top 2.5% of the salaries.

Using a z-table, we can find that the z-score that corresponds to the top 2.5% is approximately 1.96.

We can then use this z-score to find the salary level that corresponds to it:

z-score = (x - mean) / standard deviation

1.96 = (x - 50,000) / 2,500

x - 50,000 = 1.96 * 2,500

x - 50,000 = 4,900

x = 54,900

Therefore, the salary level that divides the teachers into one group that gets a raise and one that doesn't is $54,900.

The Salary of Teachers in a Particular School District Is