Suppose that the national average for the math portion of the College Board\'s S

Question

Suppose that the national average for the math portion of the College Board's SAT is 510. 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.

(a) What percentage of students have an SAT math score greater than 585? % (b) What percentage of students have an SAT math score greater than 660? % (c) What percentage of students have an SAT math score between 435 and 510? % (d) What is the z-score for student with an SAT math score of 625? (e) What is the z-score for a student with an SAT math score of 415?

Explanation / Answer

mean = 510, std. dev. = 75

(A) What percentage of students have an SAT math score greater than 585?

585 - 510 = 75

As per emparical rule 68% population lies from 1-sigma level of the mean.

Hence percentage of students have an SAT math score greater than 585 = 0.5 - 0.34 = 0.16 i.e. 16%

(B) What percentage of students have an SAT math score greater than 660?

660 - 510 = 150 i.e. 2-sigma level

As per emparical rule, 95% lies within the 2-sigma level of the mean

Hence percentage of students have an SAT math score greater than 660 = 0.5 - 0.95/2 = 0.25 i.e. 2.5%

(C)What percentage of students have an SAT math score between 435 and 510?

510 - 435 = 75

required % = 0.68/2 = 0.34 i.e. 34%  students have an SAT math score between 435 and 510.

(D) What is the z-score for student with an SAT math score of 625?

z = (625-510)/75 = 1.533

(E) What is the z-score for a student with an SAT math score of 415?

z = (415-510)/75 =1.2667

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