Question 860089
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
mean &#956; = 67 inches and standard deviation of &#963; = 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
{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)), green(line(1,0,1,exp(-1^2/2)),line(-1,0,-1,exp(-1^2/2))),green(line(2,0,2,exp(-2^2/2)),line(-2,0,-2,exp(-2^2/2))),green(line(3,0,3,exp(-3^2/2)),line(-3,0,-3,exp(-3^2/2))),green(line( 0,0, 0,exp(0^2/2))),locate(4.8,-.01,z),locate(4.8,.2,z))}}}