Suppose SAT Mathematics scores are normally distributed with a mean of 515515 and a standard deviation of 115115. A university plans to send letters of recognition to students whose scores are in the top 10%10%. What is the minimum score required for a letter of recognition? Round your answer to the nearest whole number, if necessary.
Answer
Let X is SAT mathematics score so
Given that
X~N(mean=515515,SD=115115)
University sends letter of recognition to top 10% of the students.
Let L is minimum score required for letter of recognition
So
P(X>L)=0.1
So now
From.Z table
P(Z>1.2 82)=0.1
So
This gives
L=515515+1.282*115115=663092.43
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