Question 636624
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
mean = $38,000  and SD = $7000
(A) What percentage of Americans earn below $25,000? P(z < -1) = (100-68.27)/2 = 15.87%
(B) What percentage of Americans earn above $46,000? P(z > 1) = 15.87%
For the normal distribution: 
<u>one  standard deviation from the mean accounts for about 68.27% of the set</u> 
two standard deviations from the mean account for about 95.4%
and three standard deviations from the mean account for about 99.7%.
Important to Understand z -values as they relate to the Standard Normal curve:
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))}}}