After running the QBI installer, you go to http://mywebsite/qbi to complete the installation. QBI says that the database tables have been installed, but when you click "continue", it prompts you again to install the tables.
The MySQL installer scripts originally provided with QBI 3.87 were not compatible with MySQL 5.5 or higher.
Download these new SQL script files and copy them over the existing ones in the /qbi folder on your server. Then open http://mywebsite/qbi in your browser to complete the installation. Note: QBI installers provided after Aug 25, 2012, already contain the compatible script files. If you have an older version of QBI, you will need to upgrade to v3.87.