Fungi in beech forest trees. Refer to the Applied Ecology and Environmental Research (Vol. 1, 2003) study of beech trees damaged by fungi, presented in Exercise 3.21 (p. 125). The researchers found that 25% of the beech trees in east central Europe had been damaged by fungi. Consider a sample of 20 beech trees from this area.
a. What is the probability that fewer than half are damaged by fungi?
b. What is the probability that more than 15 are damaged by fungi?
c. How many of the sampled trees would you expect to be damaged by fungi?
Exercise 3.21
Fungi in beech forest trees. Beechwood forests in East Central Europe are being threatened by dynamic changes in land ownership and economic upheaval. The current status of the beech tree species in this area was evaluated by Hungarian university professors in Applied Ecology and Environmental Research (Vol. 1, 2003). Of 188 beech trees surveyed, 49 had been damaged by fungi. Depending on the species of fungus, damage will occur on either the trunk, branches, or leaves of the tree. In the damaged trees, the trunk was affected 85% of the time, the leaves 10% of the time, and the branches 5% of the time.
a. Give a reasonable estimate of the probability of a beech tree in East Central Europe being damaged by fungi.
b. A fungus-damaged beech tree is selected at random, and the area (trunk, leaf, or branch) affected is observed. List the sample points for this experiment, and assign a reasonable probability to each one.
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