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
![\mu=820\ \ \ ,\ \sigma=200](https://tex.z-dn.net/?f=%5Cmu%3D820%5C%20%5C%20%5C%20%2C%5C%20%5Csigma%3D200)
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
, where x is minimum score that such a student can obtain and still qualify for admission at the college.
Formula for z-score =
...(i)
From normal z-value table ,
...(ii)
From (i) and (ii) , we get
![\frac{x-820}{200}=1.0364\\\\\Rightarrow\ x-820=207.28\\\\\Rightarrow\ x=207.28+820=1007.28](https://tex.z-dn.net/?f=%5Cfrac%7Bx-820%7D%7B200%7D%3D1.0364%5C%5C%5C%5C%5CRightarrow%5C%20x-820%3D207.28%5C%5C%5C%5C%5CRightarrow%5C%20x%3D207.28%2B820%3D1007.28)
Hence, the minimum score that such a student can obtain and still qualify for admission at the college is 1007.28.