Step 1 :The problem is asking for the mean and standard error of the sampling distribution for the proportion of voters who support a new fire district.
Step 2 :The mean of the sampling distribution of the proportion is equal to the true population proportion. In this case, the mean is \(0.42\).
Step 3 :The standard error of the sampling distribution of the proportion is calculated using the formula: \[SE = \sqrt{ \frac{p(1-p)}{n} }\] where p is the population proportion and n is the sample size. In this case, p = 0.42 and n = 183.
Step 4 :Substituting the given values into the formula, we get: \[SE = \sqrt{ \frac{0.42(1-0.42)}{183} }\]
Step 5 :After calculating, we find that the standard error of the distribution is approximately 0.0365.
Step 6 :Final Answer: The mean of the distribution is \(\boxed{0.42}\) and the standard error of the distribution is approximately \(\boxed{0.0365}\).