You build a monitoring utility from source and install it by hand, outside the distribution's package manager, as a plain binary with no bundled tree of its own. Under the FHS, which directory should the executable be installed into?

LPIC-1 Exam 101-500, objective 104. Devices, Linux filesystems, filesystem hierarchy standard hard

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The options

Correct /usr/local/bin

Correct. The /usr/local hierarchy is reserved for software the local administrator installs, and it is deliberately kept clear of anything the distribution's packages own.

Not correct /usr/bin

Wrong. /usr/bin holds the non-essential binaries that the distribution's package manager owns. A hand-installed file there may be overwritten or reported as unowned at the next upgrade.

Not correct /bin

Wrong. /bin is for the essential commands needed by single-user mode and by boot and repair scripts, before other filesystems are mounted. A monitoring utility is not in that class.

Not correct /opt/bin

Wrong as stated. /opt holds self-contained add-on packages, each in its own /opt/<package> directory; /opt/bin is only reserved for local administrator use and is not where a compiled build belongs.

Why

The FHS separates directories by who owns their contents. The distribution owns /bin, /sbin, /usr/bin and /usr/sbin; the local administrator owns /usr/local, which mirrors the same bin, sbin, lib, share and etc structure beneath it; and /opt is for a third-party package that keeps its own self-contained tree under /opt/<package>. Keeping locally built software in /usr/local is what allows a package upgrade to run without colliding with it. The essential-versus-non-essential split is a second axis: /bin and /sbin hold what is needed before /usr is available.

Where this comes from

Cited
manual page hier(7)

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