You intend to draw a random sample of size $n=500$ from a population whose parameter is $p=0.18$ What is the mean of the distribution of sample proportions? \[ \mu_{\hat{p}}=\square \] What is the standard deviation of the distribution of sample proportions? (Report answer accurate to 2 decimal places.) \[ \sigma_{\widehat{p}}= \] Question Help: Message instructor Submit Question Jump to Answer

Step 1 ：The mean of the distribution of sample proportions is equal to the population proportion, p. In this case, p = 0.18. So, the mean of the distribution of sample proportions, denoted as μ_p_hat, is 0.18.

Step 2 ：The standard deviation of the distribution of sample proportions can be calculated using the formula: σ_p_hat = sqrt[(p(1 - p)) / n] where p is the population proportion and n is the sample size. In this case, p = 0.18 and n = 500.

Step 3 ：Substitute the values into the formula, we get σ_p_hat = sqrt[(0.18(1 - 0.18)) / 500] = 0.017181385275931625

Step 4 ：Rounding to two decimal places, we get σ_p_hat = 0.017

Step 5 ：Final Answer: The mean of the distribution of sample proportions is \( \boxed{0.18} \). The standard deviation of the distribution of sample proportions is \( \boxed{0.017} \).