Suppose the diameter at breast height (in.) of trees of a certain type is normally distributed with μ= 8.8 and σ 2.8 , as suggested in the article “Simulating a Harvester-Forwarder Softwood Thinning” (Forest Products J., May 1997: 36–41).
a. What is the probability that the diameter of a randomly selected tree will be at least 10 in.? Will exceed 10 in.?
b. What is the probability that the diameter of a randomly selected tree will exceed 20 in.?
c. What is the probability that the diameter of a randomly selected tree will be between 5 and 10 in.?
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 exceeding 10 in.?
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