Question

in a distribution which is exactly normal 12% of the item are under 30 and 85% are under 60, find the mean and standard deviation of the distribution​

Answer 1

Given :  a distribution which is exactly normal 12% of the item are under 30 and 85% are under 60

To Find : the mean and standard deviation of the distribution​

Solution:

Mean = M

SD = D

Z score = ( Value - Mean )/SD

12% of the item are under 30

Z score for 12 % = -1.175

Value = 30

=> -1.175 = ( 30 - M) /S

=> -1.175S  = 30 - M

85% are under 60

Z score for 85 % = 1.037

Value = 60

1.037 = ( 60 - M )/S

=> 1.037S = 60 - M  

=> 2.212S = 30

=> S = 13.562

Mean  =  45.936

Standard Deviation = 13.562

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