Too many green ones? In a really large bag of M&M's, the students in Exercise 8 found 500 candies, and 12% of them were green. Is this an unusually large proportion of green M&M's? Explain.
Exercise 8
Bigger bag. Suppose the class in Exercise 6 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 6
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?