Bigger bag Suppose the class in Exercise 18 buys bigger bags of candy, with 200 M&M’s each. Again the students calculate the proportion of green candies they find.
a) Explain why it’s appropriate to use a Normal model to describe the distribution of the proportion of green M&M’s they might expect.
b) Use the 68–95–99.7 Rule to describe how this proportion might vary from bag to bag.
c) How would this model change if the bags contained even more candies?
Exercise 18
M&M’s The candy company claims that 10% of the M&M’s it produces are green. Suppose that the candies are packaged at random in small bags containing about 50 M&M’s. A class of elementary school students learning about percents opens several bags, counts the various colors of the candies, and calculates the proportion that are green.
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?