7.54 M&Ms According to the M&M website, the average percentage of brown M&M candies in a pack- age of milk chocolate M&Ms is 13%.15 (This percentage varies, however, among the different types of packaged M&Ms.) Suppose you randomly select a package of milk chocolate M&Ms that contains 55 candies and determine the proportion of brown candies in the package.

a. What is the approximate distribution of the sample proportion of brown candies in a package that con- tains 55 candies?

b. What is the probability that the sample proportion of brown candies is less than 20%?

c. What is the probability that the sample proportion exceeds 35%?

d. Within what range would you expect the sample proportion to lie about 95% of the time?