For this problem, my task is simple. I have to be able to "summarize what key concepts are being explained in the example. I have to summarize what the problem is explaining and the bottom-line concepts described in the problem."

Can you help me summarize what this problem is stating and be able to explain it in basic English? Thank you.

Suppose that we draw 1000 random samples, each of size n = 2 5, from a normal pop- ulation with a mean of 50 and a standard deviation of 2. If we calculate the mean i of each sample, then the distribution of all 1000 E values gives a good approximation to the sampling distribution of E. Figure 5.16 shows a histogram of the results of such an experiment. Notice that the 1000 sample means stack up around the population mean (pt = 50) and that variation among the sample means is smaller than variation in the population. In particular, none of the sample means fall outside the range of 48.5 to 51.5 (i.e., none are more than 1.5 units away from p). In fact, it also appears that very few sample means fall outside the interval 49 to 51; that is, they are gener- ally within 1 unit of ,u. Distribution of sample means 0.2 Frequency 100 80 0' 1 Population 60 40 20 0.0 44 46 48 50 52 54 56 48.5 49.5 50.5 51.5 Mean Figure 5. I 6 Approximating the sampling distribution of )7 (n = 25)