Question 1201631: 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 1085 and a standard deviation of 199. Scores on the ACT test are normally distributed with a mean of 20.5 and a standard deviation of 3.8. 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 1543, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! using my ti-84 plus, i get the following.
z-score that has .61 area to the left of it is equal .279319035.
use the z-score formula to find the raw score.
if the mean is 1085 and the standard deviation is 199, then you get:
.279319035 = (x - 1085) / 199.
solve for x to get x = .279319035 * 199 + 1085 = 1140.584488.
round to whole number to get 1141.
if the mean is 20.5 and the standard deviation is 3.8, then you get:
.279319035 = (x - 20.5) / 3.8.
solve for x to get:
x = .279319035 * 3.8 + 20.5 = 21.56141233.
round to 1 decimal place to get 21.6.
if the student gets a SAT score of 1543, then the z-score formula would become.
z = (1543 - 1085) / 199 = 2.301507538.
to confirm, solve for raw score using that z-score.
you get2.301507538 = (x - 1085) / 199
solve for x to get x = 2.301507538 * 199 + 1085 = 1543, confirming the calculations are correct.
use the z-score formula again to get the comparable act score.
you get 2.301507538 = (x - 20.5) / 3.8.
solve for x to get x = 2.301507538 * 3.8 + 20.5 = 29.24572864.
round to 1 decimal place to get 29.2.
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