The company that produces m&ms claims that 10% of the candies in its standard packages are green. Suppose that a class buys enough bags to sample 200 m&m candies. They calculate the proportion of green candies among 200 of these, which they choose using a simple random sampling method.

a) Under a certain condition or conditions, it is possible to model the proportion of green m&ms that you would find in a number of different random samples all of the same size by a Normal distribution with a specific mean and standard deviation. Verify that that condition or conditions are satisfied here and justify that conclusion.

b)What is the mean of the Normal distribution appropriate to model for the proportion of green m&mss in this sample of 200?

c) What is the standard deviation for the Normal distribution appropriate to approximate the probability model for the proportion of green m&ms in this sample of 200?

d) Use the 68-95-99.7 rule for Normal distributions to predict the range of proportions within which you would expect 68% of all possible examples of this same sort of same proportion to fail (of green m&ms out of a total of randomly selected 200)