The national average for the math portion of the College Board\'s SAT test is 54
ID: 3134606 • Letter: T
Question
The national average for the math portion of the College Board's SAT test is 540. 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 615? % (b) What percentage of students have an SAT math score greater than 690? % (c) What percentage of students have an SAT math score between 465 and 540? % (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
a) Xi=615, Xbar=540, s=75. Compute z score.
z=9Xi-Xbar)/s=(615-540)/75=1. Find area beyond z=1 and multiply with 100 to get required percenatge. Ans 15.87%
b) z=(690-540)/75=2. Percentage of area is 100 multiplied by area beyond z=2. Ans 2.28%
c) Find z scores corresponding to Xi=465 and 540.
z1=(465-540)/75=-1 and z2=(540-540)/75=1. Find area corresponding to respective z scores by looking areas between mean and z and then add the areas. Multiply the end result to obtain required percentage.
(0.3413+0.3413)*100=68.26%
d) z=(625-540)/75=1.13
e) z=(415-540)/75=-1.67