The zombies are timed to simultaneously send bogus data packets to the victim's server. All of this data, coming from hundreds of computers at once, blocks entry to legitimate users. It's like all Three Stooges trying to get through the door at once. There may be lots of jostling and squealing, but no one gets through until the pressure lets up. Very few legitimate calls get through and the web site gets flooded like the engine of a car.
Many companies can overcome such an attack.
For some, it is no worse than having the phone lines down for a day. There is no way of knowing if your web site will be targeted for a DoS attack. If your business can't survive the downtime, the best defense is to invest in software that alerts you when an attack begins. The software is fairly sophisticated and works with your firewall or router. If an attack is detected, the software sets up screens and filters to prevent the attack.