Good work! Quick feedback on your answers: part (a) has everything needed to describe a distribution (center, shape, and spread are mentioned, so no need for outliers/range), though you should show where the 10.75 seconds calculation came from. Part b, you’ve done all appropriate calculations.

As for your question - it’s a little hard to answer in text, but I’ll do my best. A *sampling* distribution will show us the results from lots of different individual samples taken from a population; each “dot” on a sampling distribution will represent an x-bar (or p-hat) obtained from a single *sample.* A sample or population distribution shows you *individuals*. So a sample distribution of heights would show you the individual height of each individual person in the sample. A sampling distribution of heights would show you the mean heights from multiple samples of individuals. The bigger the sample size, the more consistent those mean heights would get, hence the Central Limit Theorem saying that if n > 30, our sampling distribution is approximately normal, and standard error (a fancy way of saying standard deviation, but for samples, not individuals) decreases as *n* increases (if sample results become more consistent, variability decreases).

In theory, a sampling distribution displays all possible x-bars/p-hats we could get from all the different possible combinations of samples, and provides the basis for calculating margins of error, test statistics, or p-values.

To bring it all back around, what you calculated in part (a) is what a graph of a whole bunch of x-bars obtained from a whole bunch of separate samples of *n* = 40 eruptions selected out of the original data set of the 421 eruptions would look like. The graph would look approximately normal, with a mean of 210 and a standard error (deviation, but for samples) of 10.75. That graph would provide the basis for us to make calculations about a *single* sample if we were going to run a hypothesis test or build a confidence interval.