Help Figuring Math Problem

Question

A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1113 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.9 and a standard deviation of 4.9. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 61-percentile, find the actual SAT score.

SAT score = 

Round answer to a whole number.

What would be the equivalent ACT score for this student?

ACT score = 

Round answer to 1 decimal place.

If a student gets an SAT score of 1358, find the equivalent ACT score.

ACT score = 

Round answer to 1 decimal place.

Answer 1

mean 1113, sd = 204

what is the score that's 61st percentile?

find the z score from z tables or a z calculator

z=.279 for 61st percentile

(x-1113)/204 = z = .279

x= 204(.279)+1113

x=actual SAT score = 1169.9