Suppose that the national average for the math portion of the College Board's SAT is 533. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places. If your answer is negative use "minus sign".

(a)What percentage of students have an SAT math score greater than 608?%

(b)What percentage of students have an SAT math score greater than 683?%

(c)What percentage of students have an SAT math score between 458 and 533?%

(d)What is the z-score for student with an SAT math score of 620?

(e)What is the z-score for a student with an SAT math score of 405?