Depending on who you want to be able to execute your script, it's your job to use the chmod command to set its permissions accordingly.

It's typical to have both read and execute permission in any of the three levels of access for a script file either both on or both off - it makes little sense to allow only one of read or execute permission without the other, so your common permission settings on script files would be one of:

   rwxr-xr-x
   rwxr-x---
   rwx------