Firstly when you are installing Weblogic using generic installer, you need to make sure you have a JDK pre installed. As JDK is not shipped along with generic installer.
Generic installer is platform independent so the installation steps are common for any supported OS versions
1) Log in to the target system.
2) Add the bin directory of the appropriate JDK to the beginning of the PATH variable definition on the target system.
3) For example: PATH=$JAVA_HOME/bin:$PATHexport PATH (Unix/Linux) or
set PATH=%JAVA_HOME%/bin;%PATH% (Windows)
4) Go to the directory where you downloaded the installation program.
5) Launch the installation program by entering the following command
java -jar wlsversion_generic.jar
The installation program begins to install the software.
You can install with the administrator account.
Hope this answers your question. If yes, you can mark as either Helpful/Correct answer :-)
Actually, you don't need either. You are able to install WLS without any specific administration privileges. If you have access to create new users on this machine, go ahead and create a specific login ("weblogic" or "middleware" or something like that) and install the server using these credentials - running WLS with a login with fewer rights is actually a best practice.