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

D. 54,900

Step-by-step explanation:

We have been given that 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.

To solve our given problem, we need to find the sample score using z-score formula and normal distribution table.

First of all, we will find z-score corresponding to probability using normal distribution table.  

From normal distribution table, we get z-score corresponding is .

Now, we will use z-score formula to find sample score as:

, where,

= Z-score,

= Sample score,

= Mean,

= Standard deviation

Therefore, the salary of $54900 divides the teachers into one group that gets a raise and one that doesn't.