Final answer:
A system administrator should check the Setup Audit Trail to discover who added a field to the account page layout, as it records all setup changes made by users, including details on who made the change and when.
Step-by-step explanation:
To discover who added a field to the account page layout, a system administrator should check the Setup Audit Trail in Salesforce. The Setup Audit Trail helps in tracking the changes that have been made in the setup area of Salesforce by any user within the organization for the last 180 days. This will include the information on when the change was made and who made it, which is especially useful in determining actions like who added or modified fields and layouts.
Choice b, Review the Field History Tracking, wouldn't provide the needed information, as it tracks the value changes of a field, not the structural changes like addition. Option c, Examine the Field Usage Report, focuses on how often fields are being used and thus would not reveal who made changes to the page layout. Lastly, option d, Analyze the Field Accessibility settings, concerns who can view or edit a field but not who added it.