According to a study conducted in one city, $27 \%$ of adults in the city have credit card debts of more than $\$ 2000$. A simple random sample of $n=350$ adults is obtained from the city. Describe the sampling distribution of $\hat{p}$, the sample proportion of adults who have credit card debts of more than $\$ 2000$. Round to three decimal places when necessary.
A. Binomial; $\mu_{p}=94.5, \sigma_{p}=8.306$
B. Approximately normal; $\mu_{p}=0.27, \sigma_{p}=0.001$
C. Approximately normal; $\mu_{p}=0.27, \sigma_{p}=0.024$
D. Exactly normal; $\mu_{p}=0.27, \sigma_{p}=0.024$

Step 1 ：The problem is asking for the sampling distribution of the sample proportion. The sample proportion follows a binomial distribution, but when the sample size is large enough, it can be approximated by a normal distribution.

Step 2 ：The mean of the sample proportion is equal to the population proportion, and the standard deviation of the sample proportion is the square root of \(p(1-p)/n\), where \(p\) is the population proportion and \(n\) is the sample size.

Step 3 ：In this case, \(p = 0.27\) and \(n = 350\).

Step 4 ：Calculate the standard deviation: \(\sigma_p = \sqrt{p(1-p)/n} = \sqrt{0.27(1-0.27)/350} \approx 0.024\) when rounded to three decimal places.

Step 5 ：Therefore, the sampling distribution of the sample proportion is approximately normal with a mean of 0.27 and a standard deviation of 0.024.

Step 6 ：Final Answer: \(\boxed{\text{C. Approximately normal; } \mu_{p}=0.27, \sigma_{p}=0.024}\)