Answer: 1007.28
Step-by-step explanation:
Given : The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with
[tex]\mu=820\ \ \ ,\ \sigma=200[/tex]
If a college requires a student to be in the top 15 % of students taking this test, it means that they want the students that score 85 percentile or above.
Let X be the scores of any random student, we require
[tex]P(X<x)=0.85[/tex], where x is minimum score that such a student can obtain and still qualify for admission at the college.
Formula for z-score = [tex]z=\frac{x-\mu}{\sigma}=\frac{x-820}{200}[/tex] ...(i)
From normal z-value table , [tex]P(z<1.036)=0.85[/tex]...(ii)
From (i) and (ii) , we get
[tex]\frac{x-820}{200}=1.0364\\\\\Rightarrow\ x-820=207.28\\\\\Rightarrow\ x=207.28+820=1007.28[/tex]
Hence, the minimum score that such a student can obtain and still qualify for admission at the college is 1007.28.
