Question

The average SAT verbal score is 490, with a standard deviation of 96. Use the Empirical Rule to determine what percent of the scores lie between 298 and 586.

Answer 1

Answer:

Percent of the scores that lie between 298 and 586 = 81.86%

Step-by-step explanation:

We are given that the average SAT verbal score is 490, with a standard deviation of 96.

The empirical rule z value is given by;

                  $Z = \frac{X-\mu}{\sigma}$ ~ N(0,1)   where, $\mu$ = Population mean = 490

                                                              $\sigma$ = Population standard deviation = 96

Let X = percent of scores

So, Probability(percent of the scores lie between 298 and 586) =

P(298 <= X <= 586) = P(X <= 586) - P(X < 298)

P(X <= 586) = P( $\frac{X-\mu}{\sigma}$ <= $\frac{586-490}{96}$ ) = P(Z <= 1) = 0.84134

P(X <= 586) = P( $\frac{X-\mu}{\sigma}$ <= $\frac{298-490}{96}$ ) = P(Z <= -2) = 1 - P(Z <= 2) = 1 - 0.97725

                                                                                                = 0.02275

So, P(298 <= X <= 586) = 0.84134 - 0.02275 = 0.81859 or 81.86%

Therefore, percent of the scores that lie between 298 and 586 is 81.86% .