Question

Suppose that the national average for the math portion of the College Board's SAT is 514. 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 589? % (b) What percentage of students have an SAT math score greater than 664? % (c) What percentage of students have an SAT math score between 439 and 514? % (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:-

Mean= 514, S.D = 75

a) The percentage of students have an SAT math score greater than 589 is 0.159.

x = 589

By applying normal distruibution:-

z = 1.0

P(z > 1.0) = 0.159.

b) Percentage of students have an SAT math score greater than 664 is 0.023.

x = 664

By applying normal distruibution:-

z = 2.0

P(z > 2.0) = 0.023.

c) Percentage of students have an SAT math score between 439 and 514 is 0.341.

x₁ = 439

x₂ = 514

By applying normal distruibution:-

z₁ = - 1.0

z₂ = 0.0

P( -1.0 < z < 0) = P(z > -1.0) - P(z > 0)

P( -1.0 < z < 0) = 0.841 - 0.50

P( -1.0 < z < 0) = 0.341

d) The z-score for student with an SAT math score of 625 is

x = 625

By applying normal distruibution:-

z = 1.48

e) The z-score for a student with an SAT math score of 415 is - 1.32.

x = 415

By applying normal distruibution:-

z = - 1.32