1. Sampling distribution of mean
As shown from the example above, you can calculate the mean of every sample group chosen from the population and plot out all the data points. The graph will show a normal distribution, and the center will be the mean of the sampling distribution, which is the mean of the entire population.
2. Sampling distribution of proportion
It gives you information about proportions in a population. You would select samples from the population and get the sample proportion. The mean of all the sample proportions that you calculate from each sample group would become the proportion of the entire population.
3. T-distribution
T-distribution is used when the sample size is very small or not much is known about the population. It is used to estimate the mean of the population, confidence intervals, statistical differences, and linear regression.