It greatly depends on many factors. When you say your credit score is "average" what do you consider average?
Generally speaking, you'd need a minimum 620 to even be considered for a loan like you are looking for--and have no lates at all in the past year and no mortgage lates in the past two. Depending on teh lender, they might be looking for a score of at least 680. If you've got compensating factors, such as low debt to income ration, strong cash reserves, or verifiable and uncontrollable reasons for any late pay that aren't likely to recur, then you should be OK.
If your credit is "sloppy"--ie late pays because you didn't get around to it or you cat ran away (yes, I heard this one once--they were rejected), then you'll possibly be out of luck.
Another thing that could happen is an "offer"--they will give you a lower loan amount, or higher interest rate.
It's just going to depend on taht lender's underwriting criteria.
BTW--if your score is low (but 620 or higher) because you are over extended but have always paid on time, and this loan is going to lower your monthly payments to a more manageable DTI--you've got a good shot.
I want to add--if you can only get a lower loan amount--take it and pay off those credit cards, and set aside the difference between what you are paying now vs. the new monthly payment in a savings account. You'll be surprised how fast it will add up and you can pay cash for your home improvements.
Anne