Question: A wheel having the numbers 1 through 20 equally spaced about its circumference, is spun, and the number that is on top when the wheel comes to rest is recorded. If o is an outcome, let X(o) = the number of factors in the prime factorization of o. For example, if 7 comes up, then X(7) = 1 because 7 is prime. But X(15) = 2 because 15 = 3(5), and X(12) = 3 because 12 = 2(2)(3). By convention, 1 is not prime and has no prime factors. Determine the probability distribution of X, and the mean and standard deviation of X.