Question

Suppose that the sat math score (in a certain region) follows a normal distribution with mean 560 and standard deviation 90. You are going to take the test. Find your lowest score if you want to be among the top 10%

Answer 1

X ~ N ( µ = 560 , σ = 90 )
P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.1 = 0.9
Looking for the probability 0.9 in standard normal table to calculate critical value Z = 1.28
Z = ( X - µ ) / σ
1.28 = ( X - 560 ) / 90
X = 675.2
P ( X > 675.2 ) = 0.1