Should I rent my house to these tenants?

[Shel D.]

Hi all, I am new to all this so please pardon me if this is already discussed and common knowledge. I have my house advertised for rent and we have been getting some good traffic. Recently we got application from a young professional couple who seemed awesome. I verified there income and employment. On background/credit search, they both have good credit history but they both also have criminal background. The male applicant has minor speeding violation  but the female applicant has 3 traffic violations including no registration card etc. I was just taken aback with this discovery. Normally is it OK to rent out to tenants with some criminal findings?