Manufacturing companies strive to maintain production consistency, but it is often difficult for outsiders to tell whether they have succeeded. Sometimes, however, we can find a simple example. The candy company that makes M&M’s candies claims that 10% of the candies it produces are green and that bags are packed randomly. We can check on their production controls by sampling bags of candies. Suppose we open bags containing about 50 M&M’s and record the proportion of green candies.
a) If we plot a histogram showing the proportions of green candies in the various bags, what shape would you expect it to have?
b) Can that histogram be approximated by a Normal model? Explain.
c) Where should the center of the histogram be?
d) What should the standard deviation of the proportion be?