SOLUTION: The percentages obtained in an examination are normally distributed with mean 76% and standard deviation 15%. The top 15% of the students receive an A and the bottom 10% receives

Question 1086435: The percentages obtained in an examination are normally distributed with
mean 76% and standard deviation 15%. The top 15% of the students receive
an A and the bottom 10% receives a F and fail. Find
i) the minimum percentage to receive an A
ii) the minimum percentage to pass.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Top 15% are above z=+1.037
bottom 10% are below z=-1.645
sd is 15%, so anything more than .246 or .25 below 76 is fail, so less than 51% fails.
sd is 15% so anything more than 15.56 or .16 above 76 is pass, so 92% passes
z=(x-mean)/sd
z.10=-1.645=(x-76)/15
z.85=+1.037=(x-76)/15, solve for x
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