A housekeeping supervisor inspects rooms after the staff has cleaned them and compares their staff's performance against a checklist of items that should be cleaned, replaced, etc., according to standard operating procedure at the hotel. Over the past week she finds three rooms that have cleaning mistakes out of the $140$ rooms she has inspected. How many additional rooms should she sample to establish an average fraction defective for the $p$ chart she would like to make to monitor this process?

a$.78$

b$.93$

C$.108$

d$.133$