SOLUTION: the mean score of the students who took a mathematics test was 6. exactly 60% of the student pass the test. the mean score of the student who passed the test was 8. what is the mea

Algebra ->  Statistics  -> Describing-distributions-with-numbers -> SOLUTION: the mean score of the students who took a mathematics test was 6. exactly 60% of the student pass the test. the mean score of the student who passed the test was 8. what is the mea      Log On


   

Question 1069681: the mean score of the students who took a mathematics test was 6. exactly 60% of the student pass the test. the mean score of the student who passed the test was 8. what is the mean score of the student who failed the test?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe all that is expected is
x= mean score of the students failing the test
Since 6= mean score represents a "weighted average" of
%2260%25%22=60%2F100=0.6 of the students with a mean score of 8
and %22100%25%22-%2260%25%22=40%25=40%2F100=0.40 of the students with a mean score of x :
0.4x%2B0.6%2A8=6
0.4x%2B4.8=6
0.4x=6-4.8
0.4x=1.2
x=1.2%2F0.4
highlight%28x=3%29

A DIFFERENT EXPLANATION:
We are told that
6= mean score of the students who took the test
8= mean score of the students who passed the test
and also that
%2260%25%22=60%2F100=0.60 is the fraction of students who passed the test,
meaning that unfortunately
%22100%25%22-%2260%25%22=40%25=40%2F100=0.40 is the fraction of students who failed the test.
Let us say that
n= total number of students taking the test,
and we want to find
x= mean score of the students failing the test
Then
0.60n= number of students passing the test
0.40n= number of students failing the test
6%2An= sum of scores of all students taking the test
8%2A%280.60n%29= sum of scores of students passing the test
%280.40n%29%2Ax= sum of scores of students passing the test
So.
0.4nx%2B8%2A0.6n=6%2An
0.4nx%2B4.8n=6n
%280.4x%2B4.8%29n=6n
0.4x%2B4.8=6
0.4x=6-4.8
0.4x=1.2
x=1.2%2F0.4
highlight%28x=3%29