Question

3. High school students are faced with taking the ACT or the SAT tests to measure their readiness to start college. Quantitative SAT scores have a mean of 1509 and a standard deviation of 312 while quantitative ACT scores have a mean of 21.1 and a standard deviation of 5.

   a. A student takes the ACT and receives a score of 35 while another takes the SAT and receives a score of 2202. Which student has scored higher relatively speaking?

  b. In order to get into MIT, you need to be in the top 20% of all students who take the ACT. What is the ACT score that a student must obtain to qualify for MIT?

c. A student receives a SAT score of 1990. What percentile is the student in?

Answer 1

Solution-A:

Z score for ACT is

Z=x-mean/sd

z=35-21.1/.5

z=2.78

Z score for SAT

z=2202-1509/312

z= 2.221154

Z score for ACT is high

ACT student has scored higher relatively speaking since z score is high

b. In order to get into MIT, you need to be in the top 20% of all students who take the ACT. What is the ACT score that a student must obtain to qualify for MIT?

z score for top20%= -0.8416212

z=x-mean/sd

-0.8416212=x-21.1/5

x= -0.8416212*5+21.1

x= 16.89189

he ACT score that a student must obtain to qualify for MIT=16.89189

c. A student receives a SAT score of 1990. What percentile is the student in

z score for 1990

z=x-mean/sd

z=1990-1509/312

z= 1.541667

P(Z<1.541667)

=0.9384

93.84% percentile