To track epidemics, the Center for Disease Control and Prevention requires

physicians to report all cases of important transmissible diseases. In 2014,

a total of 350,062 cases of gonorrhea were officially reported, 53% of which

were individuals in their 20s. Assume this 53% stays the same every year.

Researchers plan to take a simple random sample of 400 diagnosed cases of

gonorrhea to study the risk factors associated with the disease. Call $\hat{p}$

the proportion of cases in the sample corresponding to individuals in their 20s.

What is the mean of the sampling distribution of $\hat{p}$ in random samples of size 400?