Final answer:
The American cockroach primarily lives outdoors and prefers warm, moist environments such as sewers and basements, but originates from outdoor habitats. Therefore, the correct option is b).
Step-by-step explanation:
The question relates to the habitat preference of a specific type of cockroach. In the context of biology and entomology, habitat preferences can provide key insights into the behavioral ecology and distribution of insect species, such as cockroaches. There are various species of cockroaches, and among the options provided – Australian, American, German, and Brown-banded – the cockroach that primarily lives outdoors is the American cockroach (Periplaneta americana).
This species is known for its preference for warm, moist environments and is commonly found in sewers, basements, and commercial buildings, but is initially from outdoor habitats. Unlike the American cockroach, the other species listed have different habitat preferences. The German cockroach (Blattella germanica), for example, is commonly found indoors, especially in kitchen areas. The mention of the correct option – the American cockroach living primarily outdoors – comes in the Final Part of the answer.