Hi,

mean of 100 and a standard deviation of 15.

3) below 70 ( 2 SDs to the left)  .05/2 = .025  0r  2.5%

4) above 115 (1 SD to the right)  .32/2 = .16  0r  16%

see graph below

For the normal distribution: 

one  standard deviation from the mean accounts for about 68% of the set ***

two standard deviations from the mean account for about 95% *** (.05% the extreems

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



 

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