The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored greater than 700.

We are given that the College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100.

Let X = percentage of students who scored greater than 700.

Since, X ~ N([tex]\mu, \sigma^{2}[/tex])

The z probability is given by;

Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1) where, [tex]\mu[/tex] = 500 and [tex]\sigma[/tex] = 100

So, P(percentage of students who scored greater than 700) = P(X > 700)

P(X > 700) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{700-500}{100}[/tex] ) = P(Z < 2) = 0.97725 or 97.72% Therefore, percentage of students who scored greater than 700 is 97.72%.