An advertiser claims that the average percentage of brown M&M'S candies in a package of chocolate M&M'S is 40%. Suppose you randomly select a package of chocolate M&M'S that contains 60 candies and determine the proportion of brown candies in the package.

(a) What is the sampling distribution of the sample proportion of brown candies in a package that contains 60 candies if the advertiser's claim is correct? (Please specify the values of the mean and standard deviation (or standard error) of the sampling distribution.) (Round your answer to four decimal places.) (2pts)

(b) What is the probability that the sample proportion of brown candies is between 39% and 43% if the advertiser's claim is correct? (Round your answer to four decimal places.) (3pts)