Final answer:
The bacterium in question is gram-negative, oxidase-negative, and lactose fermenting, indicating it is likely a member of the Enterobacteriaceae family.
Step-by-step explanation:
Using the provided dichotomous key and characteristics, the bacterium that stains pink in the gram stain, produces no color when exposed to oxidase substrate, and produces both acid and gas when inoculated in lactose broth is likely a member of the family Enterobacteriaceae. These bacteria are characterized as gram-negative, oxidase-negative, and capable of fermenting lactose with the production of acid and gas.
Since the bacterium stains pink, it is gram-negative. The absence of pigment production with oxidase substrate suggests it is oxidase-negative. The production of acid and gas in lactose broth confirms the ability to ferment lactose. Considering these biochemical characteristics, we can determine that the bacterium is classified within the Enterobacteriaceae family, which includes common gastro-intestinal tract bacteria like Escherichia coli. Laboratory tests such as IMViC can be used to further differentiate among members of this family.