Question

ACT and SAT scores are both known to be normally distributed. In 2017, the mean and standard deviation for the ACT were μ=20 and σ=6, respectively. The mean and standard deviation for the SAT were μ=1060 and σ=200, respectively. a. What ACT score would place a student in the same percentile as a student who scored 1310 on the SAT in 2010? (In other words, what ACT score is "equivalent" to an SAT score of 1310?) Round your answer to the nearest integer. b. What SAT score would place a student in the same percentile as a student who scored 14.6 on the ACT in 2010? (In other words, what SAT score is "equivalent" to an ACT score of 14.6?) Round your answer to the nearest integer.

Answer 1

Solution:

Given: ACT and SAT scores are both known to be normally distributed.

For the ACT :

μ=20 and σ=6.

For the SAT:

μ=1060 and σ=200.

Part a. What ACT score would place a student in the same percentile as a student who scored 1310 on the SAT in 2010?

x = 1310 for SAT

Find  z score for x = 1310

Now use this z score value to find corresponding ACT score:

Use following formula to find x value ( ACT score):

ACT score would place a student in the same percentile as a student who scored 1310 on the SAT in 2010 is 28

Part b) What SAT score would place a student in the same percentile as a student who scored 14.6 on the ACT in 2010?

x = 14.6 for ACT.

Find  z score for x = 14.6

Now use this z score value to find corresponding SAT score:

Use following formula to find x value ( SAT score):

Thus SAT score would place a student in the same percentile as a student who scored 14.6 on the ACT in 2010 is 880.