Duke is exhausted and plops down on the couch. Fifteen minutes after falling asleep, Duke is not awakened by the refrigerator cycling on. He is, however, awakened by his roommate opening the refrigerator door. Duke is most likely in .

Stage 2 N-REM

Explanation:

as there is different stages of sleeping process and in stage 2 of  Non -rapid eye movement sleep   person eye  movement is stop, heart beat and brain waves become slow. Person become less conscious about surrounding activities. It is light sleep  and occur between wakefulness and deep sleep . So in this example Duke is in Stage 2 , in which he is light sleep but his roommate entrance awakened him.

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