Question

Suppose that the national average for the math portion of the College Board's SAT is 547. 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 622?
	%
(b)	What percentage of students have an SAT math score greater than 697?
	%
(c)	What percentage of students have an SAT math score between 472 and 547?
	%
(d)	What is the z-score for student with an SAT math score of 630?
(e)	What is the z-score for a student with an SAT math score of 395?

Answer 1

u = 547, = 75

we have, z = (x-u)/

a)P(X > 622)

= P(z > (622-547)/75)

= P(z > 1)

= 0.1587

=> 15.87%

b)

P(X > 697)

= P(z > (697-547)/75)

= P(z > 2)

= 0.0228

=> 2.28%

c) P(473 < x < 547)

= P( (473-547)/75 < x < (547-547)/75)

= P(-1 < z <0)

= P(z <0) - P(z < -1)

= 0.5000 - 0.1587

= 0.3413

=> 34.13%

d) z score when x = 630

z = (630-547)/75

z = 1.11

e)

z score when x = 395

z = (395-547)/75

z = -2.03