Sampling Distribution of p

The distribution of the mean number of successes

The sampling distribution of $p$ is the distribution of the mean number of successes. It has a mean equal to the population proportion.

 $.75$

The mean of the sampling distribution of $p$ is equal to the population proportion. It is $225/300 = .75$.

  $.137$

The standard error of $p = \sqrt[p(1-p)/N] = \sqrt[(.75)(.25)/10] = .137$