# 1. Forest type 1 has an average diameter of 35 cm and a standard deviation of 6 cm.

01 / 10 / 2021 Statistics

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1. Forest type 1 has an average diameter of 35 cm and a standard deviation of 6 cm. Forest type 2 has an
average diameter of 25 cm and a standard deviation of 5 cm. The distribution of the diameters is normal in
both types.
a. What is the probability that a sample mean will be greater than 36 cm from type 1 if 20 trees are
measured?
b. What is the probability that a sample variance is less than 19 cm2 from type 1 if 20 trees are
measured?
c. Find the probability that the sample mean computed from 20 measurements from type 1 will exceed
the sample mean computed from 25 measurements from type 2 by at least 11 cm.
d. Find the probability that the ratio of sample variances (S1
2/S2
2) computed from 10 measurements
from type 1 (S1
2) and 8 measurements from type 2 (S2
2) will exceed 5.4.
2. The probability of finding a bark beetle infested tree in forest type 1is 0.30 and in forest type 2 is 0.35.
a. If a sample of 50 trees is taken from forest type 1, what is the probability that the proportion of beetle
attack is less than 0.20?
b. If a sample of 35 trees is taken from forest type 1and another sample of 40 from forest type 2, what is
the probability that the proportion of beetle attacked trees from type 2 will exceed the proportion from
type 1 by at least 0.1?
3. The following are some of the data collected in one of the mensuration exercises. The measurements are
volumes in m3/ha for 24 different plots:

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