According to a study conducted in one city, 34% of adults in the city have credit card debts of more than $2000. A simple random sample of n equals 350 adults is obtained from the city. Describe the sampling distribution of Modifying Above p with caret, the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary. **Understanding Sampling Distribution of Proportions**According to a study conducted in one city, 34% 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.**Options:**- **A.** Approximately normal; $ \mu_{\hat{p}} = 0.34 $, $ \sigma_{\hat{p}} = 0.001 $- **B.** Binomial; $ \mu_{\hat{p}} = 119 $, $ \sigma_{\hat{p}} = 8.862 $- **C.** Exactly normal; $ \mu_{\hat{p}} = 0.34 $, $ \sigma_{\hat{p}} = 0.025 $- **D.** Approximately normal; $ \mu_{\hat{p}} = 0.34 $, $ \sigma_{\hat{p}} = 0.025 $**Analysis:**The distribution type and parameters of $ \hat{p} $ are important statistical considerations. For a sufficiently large sample size, the sampling distribution of a proportion $ \hat{p} $ can be approximated by a normal distribution.- **Mean ($ \mu_{\hat{p}} $)**: The mean of the sampling distribution of $ \hat{p} $ is the population proportion, 0.34. - **Standard Deviation ($ \sigma_{\hat{p}} $)**: Calculated using the formula $ \sqrt{\frac{p(1-p)}{n}} $.Given these calculations, we find that the standard deviation rounds to 0.025, making option **D** the correct description of the sampling distribution: approximately normal with $ \mu_{\hat{p}} = 0.34 $ and $ \sigma_{\hat{p}} = 0.025 $.

From the provided information, Sample size (n) = 350 and proportion (p) = 0.34 The sampling distribution of sample proportion follow normal distribution.The mean and standard deviation of normal distribution can be obtained as: Thus, it is approximately normal; µp = 0.34 and σp = 0.025 Hence, the correct option is D).