Using the data above if you want to score at the 95th percen

Using the data above, if you want to score at the 95th percentile (better than 95% of students), what is the minimal score you need to earn on the Math section of the SAT?

On the SAT Mathematics section, scores range from 200 ½ 800, with a mean of italic sigma = 100. If a student is selected at random, what is the probability that their score is between 350 and 650? Using the data above, if you want to score at the 95th percentile (better than 95% of students), what is the minimal score you need to earn on the Math section of the SAT? italic mu = 500 with

Solution

So the probability that their score is between 350 and 650 is

P(350<X<650) = P((350-500)/100 <(X-mean)/s <(650-500)/100)

=P(-1.5<Z<1.5) =0.8664 (from standard normal table)

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So P(X<x)=0.95

--> P(Z<(x-500)/100) =0.95

--> (x-500)/100 =1.64 (from standard normal table)

So x= 500+1.64*100 =664