1. Suppose that a number from the set of four numbers {1, 2, 3, 4, 5} will be chosen at random with replacement each of 200 times. (a) Calculate the mean, , and standard deviation, o, of the population distribution with probability mass function f(x) = 1/5, if x = 1, 2, 3, 4, 5. (b) Approximate the probability that the average of the 200 numbers to be chosen will fall between 2.85 and 3.25