Question

Study the normal distribution graph given, in which 31% (items marked in red) are below 45 and 8% items (marked in green) are above 64 WHAT IS Z VALUE OF X =64

Answer 1

Given : normal distribution graph 31%  items  are below 45 and 8% items   are above 64

To find : Mean & Standard Deviation  , Z score for x = 64

Solution:

Let say Mean = M

& Standard Deviation   SD  = S

Z score  = ( Value - Mean)/SD

31%  items are  below 45

Z score for 31 % =  -0.496

-0.496 = ( 45 - M)/S

=> -0.495S = 45 - M

8% items above 64  => 92 % item below 64

Z score for 92 %  =  1.405

Z VALUE OF X =64   is  1.405

1.405 = (64 - M)/S

=> 1.405S  = 64 - M

=> 1.9S = 19

=> S = 10

=>  M   =     49.95

Mean = 49.95     Standard Deviation = 10

Z VALUE OF X =64   is  1.405

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