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The phrase "a specified level" is correct and usable in written English.
It can be used when referring to a particular degree, standard, or amount that has been clearly defined or identified.
Example: "To qualify for the scholarship, students must achieve a specified level of academic performance."
Alternatives: "a defined level" or "a designated level".
Exact(56)
They are: Calpers is legally bound to pay a specified level of benefits.
Prandelli hit out at the "absurd" rules that allow water breaks only if the temperature hits a specified level.
The devices sound an alarm when they detect excessive radiation and when the dose exceeds a specified level over time.
The output of the simulation model is a value of excess labor hours above a specified level.
In 1663 the laws were revised to prevent prices from falling too low, by including import duties when the home price did not exceed a specified level.
The first scheme in Germany, enacted in 1889 and based on capitalization, covered most employed persons with earnings up to a specified level.
Optimal mass distributions for mitigating shock transmission through the sandwich plate are investigated by maximizing the impulse capacity while limiting the back-face accelerations to a specified level.
These meant that, if something happened to lower the borrower's creditworthiness to a specified level, the loans could be called in.
These fees can be paid either immediately on enrolment (which earns the student a large discount) or later through income tax, when earnings reach a specified level.
Similar(2)
This can be preemptive, as when (in the markets of yester year!) a small-cap fund recites that it will close when AUM reaches a specified level.
We also illustrate the automatic retrieval of organism-specific interactomes with a specified level of support and discuss the current limitations of such retrieval.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com