Question

what proportion of u.s. residents receive a jury summons each year? a polling organization plans to survey a random sample of 500 u.s. residents to find out. let \\(\hat{p}\\) be the proportion of residents in the sample who received a jury summons in the previous 12 months. according to the national center for state courts, 15% of u.s. residents receive a jury summons each year. suppose that this claim is true. 1. calculate the mean of the sampling distribution of \\(\hat{p}\\).

Explanation:

Step1: Identify population proportion

The population proportion $p$ of U.S. residents who receive a jury summons each year is given as 15%, or $p = 0.15$.

Step2: Apply sampling distribution property

For the sampling distribution of the sample proportion $\hat{p}$, the mean $\mu_{\hat{p}}$ is equal to the population proportion $p$.
$\mu_{\hat{p}} = p$

Step3: Substitute the value

Substitute $p=0.15$ into the formula.
$\mu_{\hat{p}} = 0.15$

Answer:

0.15