The random variable x, representing the number of cherries in a cherry puff, has the following probability distribution: x 2 3 4 5 p(x = x) 0.35 0.45 0.05 0.15 (a) find the mean µ and the variance σ 2 of x. (b) find the mean µx¯ and the variance σ 2 x¯ of the mean x¯ for the random samples of 16 cherry puffs. (c) find the probability that the average number of cherries in 16 cherry puffs will be less than 2.888. use the normal distribution. round z-scores to 2 decimals. round your final answer to 4 decimals.