Hi,

P mean is 80 and the standard deviation is 8.

 z = (96-80)/8 = 2  0r (64-80)/8 = -2

(64 < x < 96) = P( -2 < z < 2) = .955  0r 955/1000 = 191/500

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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