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It is known that the true proportion of blue M&Ms produced by Mars, Inc. (the company that produces M&Ms) is 0.23. Let's say there's a fake company called Earth, Inc. that sells fake M&Ms, and we assume that the true proportion of blue M&Ms produced by Earch, Inc. is 0.4. Given a bag of 50 M&Ms, we'd like to find out if it was produced by Mars, Inc. or Earth, Inc., where we assume that the bags and the M&Ms look identical. To find this out, we consider the following simple hypotheses: Ho : p = 0.23 vs H1 : p = 0.4 where the null hypothesis is that the bag of M&Ms was produced by Mars, Inc., and the alterna- tive hypothesis is that it was produced by Earth, Inc. Suppose you suggested the following testing procedure: reject Ho if p > 0.35 (1) where p is the sample proportion of blue M&Ms in the bag. Answer the following questions. (a) (3pt) Find an approximate distribution of p under Ho. (b) (4pt) Compute the Type 1 error of the testing procedure (1). (c) (3pt) Find an approximate distribution of p under H1. (d) (4pt) Compute the power of the testing procedure (1)