The st. joe company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of 0.5 inch. a random sample of n = 50 trees is collected. what is the probability of the sample mean being less the 2.9 inches?

Solution: We are given:

μ=3.1,σ=0.5,n=50

We have to find P(Mean <2.9)

We need to first find the z score

z= (xbar-μ)/(σ/sqrt(n))

=(2.9-3.1)/(0.5/sqrt(50))

=(-0.2)/0.0707

=-2.83

Now we have to find P(z<-2.83)

Using the standard normal table, we have:

P(z<-2.83)=0.0023

Therefore the probability of the sample mean being less the 2.9 inches is 0.0023

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