3(12 pts). At a drop-in mathematics tutoring center, each teacher sees 4 to 8 students per hour. The probability that a tutor sees 4 students in an hour is 0.13; 5 students, 0.12; 6 students, 0.30; and 7 students, 0.32. Let X be the number of students per hour of a randomly selected teacher. (a) Find the probability that a tutor sees 8 students in an hour, i.e., P(X = 8). (b) Construct the probability distribution of X. (c) Find P(X 5) and P(X > 6)). (d) Find the mean of X.