Different banks take different times. One bank I can think of offered a new (and very attractive) account to customers and lots of people called them to open accounts. As the bank had given their staff lots of overtime & recruited accordingly, everything went smoothly.
At another bank this type of thing is unheard of and when they offer a savings account which pays more than any competitors, the existing staff levels are expected to cope. This inevitably leads to delays.
Your best bet would be to call the bank in question as they will have a department which deals with chasing the progress of applications.
If the application needs to overcome any obstacles, such as a chequered credit history then this may take a little longer as it might need to be referred to an underwriter for a 2nd opinion.