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
