In an engineering examination a student is considered to have failed, secured second less than 45%, between 45% and 60%, between 60% and 75% and above 75% respectively. In a particular yesr 10% of the students failed in the examination and 5% got distinction. Find the percentage of students who have got second class.(ude Normal distribution)
Answers
Given : In an engineering examination a student is considered
failed less than 45%,
second class between 45% and 60%
1st class between 60% and 75%
Distinction above 75%
10% of the students failed in the examination
5% got distinction
To Find : the percentage of students who have got second class
Solution:
Let say Mean Marks = M %
and Standard deviation = S %
Z score = ( Value - Mean)/SD
Failed 10 % for Less than 45 %
Value = 45 %
Z score for 10 % = -1.281
-1.281 = (45 - M)/S
=> -1.281S = 45 - M
5% got distinction.
=> Z score for 100 - 5 = 95 % = 1.645
Value = 75 %
1.645 = ( 75 - M)/S
=> 1,645S = 75 - M
=> 2.926S = 30
=> S = 10.253
M = 58.134
second class between 45% and 60%
Z score for 45 % = ( 45 - 58.134)/10.253 = -1281 = 10 %
Z score for 60 % = ( 60 - 58.134)/10.253 = 0.182 = 57.2 %
percentage of students who have got second class = 57.2 - 10 = 47.2 %
47.2 percentage of students got second class
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