I had followed these steps to resolve the issue:
1.) Navigated to CA ->Application Management ->Authentication Providers
Enabled anonymous access in the right zone.
2.) Went to the site were my survey list is and navigated to
Site Settings-> Advanced Permissions->Settings>Anonymous Access
selected the option List and Libraries
3.) Then I navigated to my Survey List->Settings->Permission for the List->Actions Edit permission, broke the inheritance, then navigated to Settings->Anonymous Access
But the Anonymous user options were greyed out.
So I verified all the above steps again .But found no mistakes.
Then I went to Survey List -> Settings -> Advanced Settings
Since I selected the option which allows users to view only their response, the anonymous user options in the list setting was greyed out. Once I changed this option to "All Responses", I was able to check the appropriate box in the survey list anonymous settings page.