Question

Suppose that the national average for the math portion of the College Board's SAT is 526. 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 6267 3% (b) What percentage of students have an SAT math score greater than 726? (e) What percentage of students have an SAT math score between 426 and 526? (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?

Answer 1

a) P (X > 626) = P(X> 626) x-μ-626-μ 626-526 100 -0.1587 15.87% since area under standard normal table b) P (X >726)= P (X >726) 726-526 100 =P(Z > 2) -0.02275-2.28% since area under standard normal table 426-526 100 526-526 100 = P(-1 <Z < 0) = P(Z < 0)-P(Z <-1) -0.5-0. 15866-0.34 134-34.13% from normal distribution tables d)Z-score= 620-526 100 e) Z -score -405-526 score =-1 -=-1.21 100