The College Board reported that SAT scores in the early 2000 s were normally distributed with mean 1026 and standard deviation 210 . Refer to the table of values $\triangle$ Area Under the Standard Normal Distribution as needed.
Part 1 of 2
(a) What percent of students scored over $606 ?$
$97.7 \%$ of students scored over 606 . (Round to the nearest tenth of a percent.)
Part: $1 / 2$
Part 2 of 2
(b) Out of every 500 students, how many scored between 606 and 1446 ?
We expect about SAT scores between 606 and 1446 .

Step 1 ：Find the z-scores for 606 and 1446 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 ：Calculate the z-scores: \(z_1 = \frac{606 - 1026}{210} = -2.0\) and \(z_2 = \frac{1446 - 1026}{210} = 2.0\)

Step 3 ：Use the standard normal distribution table to find the percentage of students who scored above 606: \(P(z > -2.0) = 0.9772\)

Step 4 ：Calculate the percentage of students who scored between 606 and 1446: \(P(-2.0 < z < 2.0) = 0.9772 - 0.0228 = 0.9544\)

Step 5 ：Find the number of students out of 500 who scored between 606 and 1446: \(500 \times 0.9544 = 477.2\)

Step 6 ：\(\boxed{\text{(a) 97.7\% of students scored over 606.}}\)

Step 7 ：\(\boxed{\text{(b) We expect about 477 students to have SAT scores between 606 and 1446 out of every 500 students.}}\)