Question

The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 660 and a standard deviation of 220. If a college requires a student to be in the top 20 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?

Answer 1

X ~ N ( µ = 660 , σ = 220 )
P ( X > x ) = 1 - P ( X < x ) = 1 - 0.2 = 0.8
To find the value of x
Looking for the probability 0.8 in standard normal table to calculate Z score = 0.8416
Z = ( X - µ ) / σ
0.8416 = ( X - 660 ) / 220
X = 845.152
P ( X > 845.152 ) = 0.2