Respuesta :
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 [tex]0.975(1-0.025)[/tex] using normal distribution table.
From normal distribution table, we get z-score corresponding is [tex]1.96[/tex].
Now, we will use z-score formula to find sample score as:
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z[/tex] = Z-score,
[tex]z[/tex] = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation
[tex]1.96=\frac{x-50,000}{2,500}[/tex]
[tex]1.96*2,500=\frac{x-50,000}{2,500}*2,500[/tex]
[tex]4900=x-50,000[/tex]
[tex]4900+50,000=x-50,000+50,000[/tex]
[tex]54900=x[/tex]
Therefore, the salary of $54900 divides the teachers into one group that gets a raise and one that doesn't.
