The general rule of thumb - I first came across it with Discover but it applies to a lot of other lenders too - is that the more specific the APR quote is, the better your chances of being approved are. When you try out a lender's pre-approval site, what you're looking for is either a small range between lowest and highest APR's (a difference of 3% to 4%), or, even better, a single-figure quote such as the one you cited in the OP. If you get an 8% or 10% spread between lowest and highest APR's, you can generally take it as a given that what you've gotten is a pure marketing offer; you might get approved if you apply, certainly, but at that point, with figures like that, you apply at your own risk. It's pretty odd that the bank would need to take 4 weeks to do a manual review, but if your credit reports and scores are overall good, I'd say optimism is warranted.
