Then I look at the distribution of p_i's and find that it's skewed. In this scenario,

1. Is the resampling distribution of the parameter

**supposed**to be symmetric, and therefore I should suspect something has gone wrong? In this case how do I get the point and interval estimates for p? My current thought is that it may be possible for even the resampling distribution to get skewed if the population distribution is heavily skewed to begin with

2. If it's acceptable for the resampling distribution to be skewed, should I use the mode instead of the mean or median as the point estimate? Usually we just say, take the mean of the resampling distribution as your point estimate. But in the presence of outliers, common wisdom says take the medium. But also for probability distributions, it's usually advised to take the mode as a point estimate. So which is it?