To address questions related to this scenario, it's essential to understand that this falls under the concept of binomial probability, given that the outcome for each individual adult is either "drinks coffee" or "does not drink coffee."

1. Binomial Distribution Characteristics:

   • Number of trials, $n = 250$.
   • Probability of success (an individual drinks coffee), $p = 0.63$.
   • Probability of failure (an individual does not drink coffee), $q = 1 - p = 0.37$.

2. Questions You Might Explore:

   a. Probability of Exactly $k$ Coffee Drinkers in the Sample: To find the probability that exactly $k$ U.S. adults in the sample drink coffee, use the binomial probability formula: $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$ where $\binom{n}{k}$ is the binomial coefficient, calculated as: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$

   b. Expected Value and Standard Deviation:

   • The expected number $E(X)$ of coffee drinkers: $E(X) = np = 250 \times 0.63 = 157.5$

   • The standard deviation $\sigma$ of the distribution: $\sigma = \sqrt{np(1-p)} = \sqrt{250 \times 0.63 \times 0.37} \approx 7.6494$

3. Normal Approximation: When $n$ is large, a binomial distribution can be approximated by a normal distribution with mean $\mu = np$ and standard deviation $\sigma = \sqrt{np(1-p)}$.

   • Use continuity correction if using the normal approximation to find probabilities.

For specific probability calculations, you would need to plug in the appropriate values of $k$ to use the binomial or normal approximation formulas. If you have specific probability questions in mind, feel free to ask!