SOLUTION: in a certain distribution of numbers, the mean is 80 and the standard deviation is 8. At least what fraction of the numbers are between the following pairs of numbers. Give answers

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Question 852547: in a certain distribution of numbers, the mean is 80 and the standard deviation is 8. At least what fraction of the numbers are between the following pairs of numbers. Give answers as common fractions reduced to lowest terms.
64 and 96
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

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