The correct answer is: Only assumption II is implicit.
The statement “Beware of dogs, our dogs do not bark, but they are trained to distinguish between genuine guests and intruders” does not provide enough information to support assumption I, that barking dogs bite rarely. It is possible that barking dogs bite often, but that our dogs are an exception. The statement also does not provide enough information to support assumption II, that our dogs could be dangerous for intruders. It is possible that our dogs are friendly and would never harm anyone, even an intruder. However, the statement does suggest that our dogs are trained to distinguish between genuine guests and intruders, which means that they are likely to be more aggressive towards intruders than towards genuine guests. Therefore, the only assumption that is implicit in the statement is assumption II.