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