A hotel guest satisfaction study revealed that $32\%$ of hotel guests experienced$$ better$-$than$-$expected quality of sleep at the hotel. Among these$$ guests, $48\%$ stated they would$$ "definitely" return to that hotel brand. In a random sample of $15$ hotel$$ guests, consider the number$($x$)$ of guests who experienced$$ better$-$than$-$expected quality of sleep and would return to that hotel brand.