Question 629305
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi
average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with SD =  15 minutes
Assume that the commute times are normally distributed. 
What proportion of commutes would be: between 45 and 75 minutes? 68.2%
 {{{z = (45-60)/15 = -15/15 = -1}}}  and {{{z = (75-60)/15 = 15/15 = 1}}}

For the normal distribution: 
one  standard deviation from the mean accounts for about 68.2% of the set ****
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))}}}