To be honest, for non-priority processing, some people have got it approved very quickly, in just a couple of days, but for others it took longer, so nobody can tell you how long it may take. Considering you have got the email stating it's been assigned to an entry clearance officer, it shouldn't be long. Sometimes, they don't even send this email out.
My application arrived at the consulate today. Here's my timeline so far:
Sept 2, applied online
Sept 9, biometrics appointment, purchased priority, usps expressed the application package (opted for no weekend delivery and yet usps still attempted to deliver it on Sat)
Sept 10, USPS left notice at the Consulate
Sept 12, Email confirming application has arrived safely and will be processed priority.
Now just waiting and second guessing everything. I'm driving myself crazy. I can't focus or do anything.
Finger crossed & good luck to everyone