Install Error: The directory sites/default/files is not writable

Hello all. I am attempting to install Drupal 7.34 on an EC2 instance running RHEL. With root access, I've taken the following steps:

In /var/www/html I execute: drush dl drupal to download Drupal.

I then follow Drupal's install instructions:

mv drupal-7.34/* ./
mv drupal-7.34/.htaccess ./
mv drupal-7.34/.gitignore ./
cp sites/default/default.settings.php sites/default/settings.php
chmod a+w sites/default/settings.php
chmod a+w sites/default
cd ..
chown -R apache:apache html

In the browser, I navigate to http://myhost/install.php. In the "Verify requirements" step of the install process I receive the following error:

The directory sites/default/files does not exist.

So, I take then take the following steps:

mkdir html/sites/default/files
chmod a+w html/sites/default/files
chown apache:apache html/sites/default/files

When I attempt the install process I now get the following error:

The directory sites/default/files is not writable.

What am I missing here? The sites/default/files directory exists and is writable. I've searched up and down for a solution without luck. Any guidance is much appreciated.