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nlexa [21]
3 years ago
15

The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation o

f $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
Mathematics
1 answer:
andrey2020 [161]3 years ago
4 0

Answer:

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 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=\frac{x-\mu}{\sigma}, where,

z = Z-score,

z = Sample score,

\mu = Mean,

\sigma = Standard deviation

1.96=\frac{x-50,000}{2,500}

1.96*2,500=\frac{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.

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