Suppose the diameter at breast height (in.) of trees of a certain type is normally distributed with 8.8 and 2.8, as suggested in the article "simulating a harvester-forwarder softwood thinning" (forest products). a. what is the probability that the diameter of a randomly selected tree will be at least 10in.? will exceed 10in.?
b. what is the probability that the diameter of a randomly selected tree will exceed 20in?
c. what is the probability that the diameter of a randomly selected tree will be between 5 and 10in.?
d. what value c is such that the interval (8.8 − c, 8.8 + c) includes 98% of all diameter values?
e. if four trees are independently selected, what is the probability that at least one has a diameter that exceeds 10in.?