Question

Suppose that the national average for the math portion of the College Board's SAT is 518. 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 618?
	%
(b)	What percentage of students have an SAT math score greater than 718?
	%
(c)	What percentage of students have an SAT math score between 418 and 518?
	%
(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

Solution :

Given that,

Using Empirical rule,

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

P( - 3< X < + 3) = 99.7%

(a)

P(X > 618) = 1 - P(X < 618) = 1 - 0.84 = 16%

(b)

P(X > 718) = 1 - P(X < 718) = 1 - 0.975 = 2.5%

(c)

P(418 < X < 518) = P(X < 518) - P(X < 418) = 0.5 - 0.16 = 34%

(d)

z = (x - ) / = (625 - 518) / 100 = 1.07

(e)

z = (x - ) / = (415 - 518) / 100 = -1.03