Question

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.

Answer 1

Answer:

Percentage of students who scored greater than 700 = 97.72%

Step-by-step explanation:

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($\mu, \sigma^{2}$)

The z probability is given by;

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

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

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