Another teacher decides to average the heights of all 15-year-old male students in his classes throughout the day. By the end of the day, he has measured the heights of 57 boys and calculated an average of 68.1 inches (172.97 centimeters; remember, for this population μ = 67 inches and  σ = 3.19 inches).

a. Calculate the mean and the standard error of the distribution of mean heights.

b. Calculate the z statistic for this group.

c. What percentage of groups of boys would we expect to have mean heights taller than this group, based on samples of this size (57)? 

d. How often do mean heights equal to or more extreme than 68.1 inches occur in this population?

e. How does this result compare to the statistical significance cutoff of 5%?