Lets say there is a company of workers and the weekly overtime work of an employee follows a normal distribution. I know the standard deviation and mean. Now the company with a view to reducing the cost of overtime work wishes to set a maximum weekly overtime allowance which should not be exceeded by more than a given number of employees.
My question is how can I go about finding this limit? My thinking was to use Feller's tail bound
$$\frac{1}{\sqrt{2\pi} x} e^{−x^2/2},$$
where $x$ is the given number of employees. Is this the right formula I should use?