Question

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

Answer 1

D. 54,900

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
`0.975(1-0.025)` using normal distribution table.

From normal distribution table, we get z-score corresponding is
`1.96`.

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

`z=(x-\mu)/(\sigma)`, where,

`z` = Z-score,

`z` = Sample score,

`\mu` = Mean,

`\sigma` = Standard deviation

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

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

`4900=x-50,000`

`4900+50,000=x-50,000+50,000`

`54900=x`

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