Question 10, 12.5.57 HW Score: $63.64 \%, 7$ of 11 12.5 points Points: 0 of 1 Save Assume that the mathematics scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100 . What percent of students who took the test have a mathematics score between 570 and 670 ? Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. $\square \%$ of students who took the test have a mathematics score between 570 and 670 . (Round to two decimal places as needed.)

Step 1 ：Convert the scores to z-scores using the formula: \(z = \frac{X - \mu}{\sigma}\), where \(X\) is the score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 2 ：For 570: \(z1 = \frac{570 - 500}{100} = 0.7\)

Step 3 ：For 670: \(z2 = \frac{670 - 500}{100} = 1.7\)

Step 4 ：Use the z-table to find the percentage of students who scored below a certain z-score. To find the percentage of students who scored between 0.7 and 1.7, subtract the percentage of students who scored below 0.7 from the percentage of students who scored below 1.7.

Step 5 ：From the z-table: \(P(Z < 0.7) = 0.7580\) and \(P(Z < 1.7) = 0.9545\)

Step 6 ：The percentage of students who scored between 570 and 670 is: \(P(0.7 < Z < 1.7) = P(Z < 1.7) - P(Z < 0.7) = 0.9545 - 0.7580 = 0.1965\)

Step 7 ：\(\boxed{19.65\%}\) of students who took the test have a mathematics score between 570 and 670.