The exact time varies. Here is the basic pattern:
The committee interviews the applicant.
The committee interviews the references provided by the applicant.
The committee prepares a report for the lodge, and delivers it.
The lodge normally votes at the same meeting, when the report is delivered.
Then the applicant is notified.
It could be a week or up to a month. If the lodge is closed all summer long, and committee completes their investigation in May, it could be September before the applicant is notified.
Be patient.