The campaign director for a Texas governor's candidate is planning a multi-stage sample survey. In the first stage, the director will randomly choose $15$ counties. The partial histogram below shows the population by county for Texas (the five highest outlier counties have been omitted).
The average population for all $254$ counties is $99,423$ people with a standard deviation of $354,429$ people.
Describe the sampling distribution of the mean population for samples of $15$ counties.