Hi,

mean μ = 67 inches and standard deviation of σ = 3.6 inches. A random sample of 16 heights is obtained.

s = 3.6/sqrt(16) = .9

P(x<63) = P(z < (-4/.9))= P(z<-4.44) = 0.000004

Yes, that is quite a ways to the left :)

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right



 

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