15% of candidates passed with distinction while 25% of them failed. It is known that a candidate fails if he obtain less than 40 marks while he must obtain at least 75 marks in order to pass with distinction. And the mean and standard deviations of the distribution of marks assuming this to be normal
Answers
Given : 15% of candidates passed with distinction while 25% of them failed
To find : mean and standard deviations of the distribution of marks assuming this to be normal
Solution:
15% of candidates passed with distinction
at least 75 marks in order to pass with distinction
=> for more than 75 marks percentage = 15 % => 85% got upto 75 marks
z score = 1.036
25% of candidates failed
failed if he obtain less than 40 marks
=> for less than 40 marks percentage = 25%
z score = -0.674
Z score = ( value - Mean)/SD
=> 1.036 = (75 - Mean)/SD
=> 1.036SD = 75 - mean
-0.674 = (40 - Mean)/SD
=> -0.674SD = 40 - Mean
=>1.71SD = 35
=> SD = 20.5
=> mean = 53.8
Mean = 53.8 and SD = 20.5
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