SOLUTION: The result of an exam score for a given class is normally distributed. If the mean score is 85 points and the standard deviation is equal to 20 points, find the cutoff passing g

Question 1115892: The result of an exam score for a given class is normally distributed. If the mean score is
85 points and the standard deviation is equal to 20 points, find the cutoff passing grade
such that 83.4% of those taking the test will pass.
Found 2 solutions by Boreal, rothauserc:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
We want the 83.4%ile or 0.8340
The lowest grade to pass will be at the 16.6%ile or 0.1667
on the z-table this is at -0.97
z=(x-mean)/sd
-0.97=(x-mean)/20
-19.4=x-85
x=65.6 cutoff

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we want the z-score associated with 1-0.834 = 0.166 probability
:
that z-score is -0.97, then
:
-0.97 = (X - 85) / 20
:
X - 85 = -19.4
:
X = 65.6
:
******************************************************
the cutoff grade is 65.6 approximately 66, this means
:
anyone getting a grade of 66 or higher passes
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:
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