We need to know more about your environment to answer this question.

Thanks very much for responding. What exactly do you need to know? These are not managed just standalone computers setup with one admin account and one standard account. The admin account is created first and all programs including Firefox are installed then a standard account is created for the users to work out of. From within this account Firefox can download the update but then asks the users to provide the admin credentials to install the update.

Hello, I think they are usually multiple updates that need to be done to the browser it will ask for admin rights to update them. Once it’s done it will stop asking. You can restrict auto-updates if you don't want to see this.

It's not a question of not wanting to see the prompt for admin credentials. I would like it to update without user intervention when used in a Standard account. This works no problem if used in an Admin account. I have installed Chrome on a couple and it auto updates in Standard accounts all by itself without user intervention. It happens every update and it asks for admin username and password every time. It has always been this way in Standard accounts on a Mac for us.

Just to update incase anyone else is having the same issue. Reinstalling Firefox while logged into the Standard account and not an Admin account solved the issue.