Question 623802
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Hi,  
A distribution has a standard deviation of   12.
 Find the z-score for each of the following locations in the distribution.
yes: z= (data point- mean)/standard deviation.
 a. Above the mean by 3 points.  z =  3/12 = 1/4
 b. Above the mean by 12 points. z = 12/12  = 1
 c. Below the mean by 24 points. z = -24/12 = -2
 d. Below the mean by 18 points. z = -18/12 = -3/2
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))}}}
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 95.5%
and three standard deviations from the mean account for about 99.7%.