In a large statistics class, the professor has each person toss a fair coin 15 times and calculate the proportion of their tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions.

a) What shape would you expect this histogram to be? Why?

b) Where do you expect the histogram to be centered?

c) How muck variability would you expect among these proportions?

d) Explain why a Normal model should not be used here.