Question 926296
For the normal distribution: Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  
Area under the standard normal curve to the left of the particular z is P(z)
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))}}}
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one  standard deviation from the mean accounts for about 68% of the set 
two standard deviations from the mean account for about 95%
and three standard deviations from the mean account for about 99.7%.
.......
mean of 100 and a standard deviation of 16

a)between 68 and 132: (2SDs on either side of mean) 95%
 b)between 68(-2SDs) and 100:  50% - 95%/2 
 c)above 116 (1SD):  50% +   68%/2
 d)below 68(-2SDs):  (100%-95%)/2
 e)above 148 (3Sds):   (100%-99.7%)/2