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 529. The College Board periodically rescales the test scores such that the standard deviation is approximately 50. 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 579?

(b) What percentage of students have an SAT math score greater than 629?

(c) What percentage of students have an SAT math score between 479 and 529?

(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 = 529

sd = 50

Z = (X - 529)/50

a) P(X > 579)

=P(Z >(579 -529)/50)

= P(Z > 1) = 0.1587 = 0.16

b)

P(X > 629)

= P(Z > 2) = 0.0228

= 0.02

c)

P(479 <X< 529)

= P(-1 <Z< 0)

= 0.3413

=0.34

d)

z = (625 -529)/50

= 1.92

e)

z =(415 -529)/50

= -2.28

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