Problem 2-23 Suppose that the national average for the math portion of the Colle

Question

Problem 2-23

Suppose that the national average for the math portion of the College Board's SAT is 517. 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 592? (b) What percentage of students have an SAT math score greater than 667? (c) What percentage of students have an SAT math score between 442 and 517? (d) What is the z-score for student with an SAT math score of 620? (e) What is the z-score for a student with an SAT math score of 405?

Explanation / Answer

a) P(X > 592)

= P(z > (592 - 517)/75)

= P(z > 1)

= 16%

b) P(X > 667)

= P(z > (667 - 517)/75)

= P(z > 2)

= 2.5%

c) P(442 < X < 517)

= P(-1 < z < 0)

= 34%

d) z score for 620 = (620 - 517)/75 = 1.37

e) z score for 405 = (405 - 517)/75 = -1.49

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