SUPP 4.1 A weight distribution for males in a certain population is approximately normal with mean mu=170 pounds and standard deviation sigma = 30 pounds. 25 men are selected. We are interested in the distribution of the average xbar of 25 men if we repeated this study many times.

a) Describe the distribution of xbar, the average weight. Where is it centered? What is the value of the standard deviation of the mean?

b) Find an xbar value that is larger than 95% of the xbars. You may find it helpful to mark this value on your sketch.

c) If you found that xbar value in Part b in your first trial of n=25, would you be surprised? Would that xbar value seem unusual?

d) If we increased the sample size to n=100, describe how the distribution of the xbar values would change. Explain very briefly.