1. A forestry company planted a population of Douglas fir trees 30 years ago. To
ID: 3126195 • Letter: 1
Question
1. A forestry company planted a population of Douglas fir trees 30 years ago. Today, the trunk diameters of these trees have a mean of 6.87 inches and a standard deviation of 1.07 inches.
a. Suppose you randomly sample 40 of these fir trees and measure their trunk diameters. What is the probability of getting a sample mean diameter greater than 7.5 inches?
b. Did you need to assume anything about the shape of the distribution of trunk diameters for your calculation in part (a)? If so, what must be assumed? If not, explain why.
Explanation / Answer
Mean ( u ) =6.87
Standard Deviation ( sd )=1.07
Number ( n ) = 40
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)
a.
P(X > 7.5) = (7.5-6.87)/1.07/ Sqrt ( 40 )
= 0.63/0.169= 3.7238
= P ( Z >3.7238) From Standard Normal Table
= 0.0001
b.
the shape of the distribution is assumed to normal distribution and the standard
normal variate is as Z= X- u / sd ~ N(0,1)
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