The distribution of SAT scores is normal with m 500 and s

The distribution of SAT scores is normal with m = 500 and s = 100.

            a.         What SAT score, X value, separates the top 12% of the distribution from the rest?

            b.         What SAT score, X value, separated the top 52% of the distribution from the rest?

Solution

mean : 500

standard deviation: 100

a) P(x)=> 12%

x=? so the probability P=>0.12 z= (x-500)/((100)) =1.17

x= 1.17(100) +500 = 617

b) P(x)=> 54% we have that the normal

x=? so the probability P=>0.02 z= (x-500)/((100)) = 2.05

x= 2.05(100) +500 = 705

we have that the probability includes more than 52% and we know that the normal distribution is split into two sections with 50% in each is why we subtract the 50% to 52%