I find it highly unlikely that it happened at all. There are so many problems with the whole story, it doesn't make sense.
Modern shipbuilders would have a hard time making a boat that big out of wood, using modern technology like iron or steel as reinforcement. There was such a ship that was built in 1909 called the Wyoming. It didn't do well in heavy seas, sank, and killed all on board. This boat needed pumps to constantly pump out the water due to the stress the shifting seas have on wooden boats. Using steam engines, they were able to use a small crew of 11.
http://en.wikipedia.org/wiki/Wyoming_(schooner)
Now Noah, if he existed, was supposed to have lived in the Bronze age. No steam engines, no steel, no iron. Only copper, bronze, wood, pitch and four sons.
Modern shipbuilding takes years. It would have taken much longer for only five people, who don't have access to modern techniques or modern tools. Just gathering the materials would have taken years, not to mention building it. Not to mention gathering all of the animals from the North American prairie dog, to the antarctic penguin, from the Australian Koala, to Komodo Dragon.
It's so implausible.
We haven't even talked about the geological record.