SOLUTION: 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.

Question 1141586: 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 1070 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number. SAT score =
(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =
(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number.

Go to a z-table and find the z-score that corresponds to 0.51. Doing so, we find that a z-score of 0.2 = 0.5080 and a z-score of 0.3 = 0.5120. If you split the difference, a z-score of 0.25 would correspond to a value of 0.51.

So, we are looking for an SAT score that is 0.25 standard deviations above the mean. Since one standard deviation is 204, an SAT score that is 0.25 standard deviations above the mean is 1070 + (0.25 * 204)...or 1121.

(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place.

Same as above. Go to a z-table and find the z-score that corresponds to 0.51. Doing so, we find that a z-score of 0.2 = 0.5080 and a z-score of 0.3 = 0.5120. If you split the difference, a z-score of 0.25 would correspond to a value of 0.51.

We are looking for an ACT score that is 0.25 standard deviations above the mean. Since one standard deviation is 5.2, an ACT score that is 0.25 standard deviations above the mean is 19.1 + (0.25 * 5.2)...or 20.4.

(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place.

Compute how many points above the mean a score of 1417 is: 1417 - 1070 = 347.

Compute how many standard deviations above the mean 347 points is: 347/204 = 1.70.

Taking the numbers from the ACT test, compute how many points above the mean 1.70 standard deviations is:

x/5.2 = 1.70.

x = 8.84.

Add 8.84 to the mean of 19.1 to get an answer of 27.94...rounded down to 27.9.
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