Suppose the diameter at breast height(in.) of trees of a certain type is normally distributed with $\mu=8.8$ and $\sigma=2.8$, 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.?
• What value $c$ is such that the interval $(8.8-c,8.8+c)$ includes $98\%$ of all diameter values?
   

Remark:

For the definition of DBH(Diameter at Breast Height), we can refer to https://www.thoughtco.com/what-is-diameter-breast-height-1341720 .