Answer:
$43,920.
Step-by-step explanation:
We have been given that the salaries of elementary school teachers in a particular country are normally distributed with a mean of $38,000 and a standard deviation of $4,000.
We will use the normal distribution table to solve our given problem. From normal distribution table, we need to find the z-score corresponding to the top 7% or z-score corresponding to probability 93% (0.93).
From normal distribution table, we get our required z-score as 1.48.
Now, we will use z-score formula to solve for sample score as:
[tex]z=\frac{x-\mu}{\sigma}\\\\1.48=\frac{x-38000}{4000}[/tex]
[tex]1.48*4000=\frac{x-38000}{4000}*4000[/tex]
[tex]5920=x-38000[/tex]
[tex]5920+38000=x-38000+38000[/tex]
[tex]43920=x[/tex]
Therefore, the cutoff salary for teachers in the top 7% is $43,920.
