A box of beer contains 24 bottles. Suppose a beer bottle has mean weight of 20 oz and a standard deviation of 0.5 oz. (a) What is the mean and variance for the weight of the beer box if we assume that the weight of the 24 bottles are independent of each other. Cb) What is the mean and variance of the average weight of the beer bottles? (c) What is the approximate distribution for the average weight of the beer bottles? Give reasons for your answer and specify the approximate distribution. (d) If we assume that the weight distribution of a beer bottle has a normal distribution, tie. X ~N {2 0,0. 52}, what is the exact distribution of total weight for the box of beer