The above section was crystal clear to me. With a population with sample means x̅1, x̅2, x̅3, x̅4, x̅5, and, x̅ for example, the sampling distribution involves all the averages. It follows that the sampling distribution of the sample means would give the average of the entire population. Moreover, the standard deviation of the sample means is the same as the standard deviation of the population divided by the square root of the sample size (n). And this value is the standard error of the mean.
However, the topic of finding probabilities was clear as mud. In general, with a random variable X with a normal distribution, to find the probability that it falls within a given interval one needs to calculate the area under the normal curve for that particular range. Whereas this statement is clear and direct, I do not seem to understand how to calculate the area under the curve.
Response to Nicolas Wagoner
I concur to some extent that Chapter 5 was challenging than the rest. However, it is not the entire chapter that was challenging. The part of calculating the mean of samples and the distribution are not so different from the usual computation of the averages. Besides, the central limit theorem is not very complicated. I must agree that calculating Z-score and the x-value under the normal distribution curve was indeed challenging. The same case occurs with finding probabilities for normal distribution. The examples given do not seem clear, and the method for calculating the area under the curve. By revisiting the entire chapter and also doing further research on the same would help in understanding the concepts.
