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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

User Fireflight
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1 Answer

2 votes

Answer:

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.

User Europeuser
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