4. (18 pts) Suppose that the diameter of trees (in inches) of a certain type is normally distributed with u = 8.8 and o = 2.8. Answer the following questions. Please provide answers to 4 significant digits. When using the standard normal table, find the closest number to the one that you are looking for, if it is not available exactly. (a) What is the probability that the diameter of a randomly selected tree will be between 5 and 10 inches? (3 pts) (b) What is the diameter that 25% of the trees exceed? (4 pts)(c) If four trees are independently selected, what is the probability that at least one has a diameter exceeding 10 inches? {4 pts) (d) What value of c is such that the interval (8.8 C, 8.8 + 6) includes 93% of all diameter values? (4 PE} (e) What is the expected area of the cross section of the tree? [H.int: the area of the crosssection is given by 11' times the square of the radius, where the radius is half of the diameter] (3 pt)