Suppose you were to draw all possible samples of size 36 from a large population with a mean of 650 and a standard deviation of 24. You then compute the mean (x) for each sample. From the long list of sample means that you produce, you want to create the sampling distribution of the sample mean, which will assign probabilities to all the possible values of x.
a. Sketch a graph of the sampling distribution that you would expect to produce and center it properly.
b. What % of the x values in the sampling distribution would be within ± 1 standard deviation (that is, within ±1σx–) of the center of the distribution within 2 standard deviations?
c. If you were to randomly select one sample of size 36 from the population here, how likely is it that the sample mean would have a value between 645 and 655 a value greater than 660?