Question

Suppose that the national average for the math portion of the College Board's SAT is 516. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. 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 616?
	%
(b)	What percentage of students have an SAT math score greater than 716?
	%
(c)	What percentage of students have an SAT math score between 416 and 516?
	%
(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?

Answer 1

a) X=616

= 15.87%

Using Empirical rule: P(X>616)= 0.16 or 16%

b) X=716

= 2.28%

Using Empirical rule: P(X>716) = 0.0225 or 2.25%

c)

or 34.13%

Using Empirical rule: = 0.34 or 34%

d) X=625

f) X=415