Step 1 :The question is asking for the sampling distribution of the proportion of adults who do not own a credit card. The shape of the distribution can be determined by checking the conditions for normality.
Step 2 :The mean of the sampling distribution is the same as the population proportion, which is \(0.17\).
Step 3 :The standard deviation of the sampling distribution can be calculated using the formula for the standard deviation of a proportion, which is \(\sqrt{p(1-p)/n}\), where p is the population proportion and n is the sample size.
Step 4 :Substitute the given values into the formula: p = 0.17 and n = 500.
Step 5 :Calculate the standard deviation: \(\sigma_p = \sqrt{0.17(1-0.17)/500} = 0.016798809481626965\).
Step 6 :Round the standard deviation to three decimal places: \(\sigma_p = 0.017\).
Step 7 :Final Answer: The standard deviation of the sampling distribution of \(\hat{p}\) is \(\boxed{0.017}\).