A study was conducted on students from a particular high school over the last 8

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 admittance. Scores on the SAT test are normally distributed with a mean of 1020 and a standard deviation of 194. Scores on the ACT test are normally distributed with a mean of 22.3 and a standard deviation of 3.9. 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 70-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 1466, find the equivalent ACT score.
ACT score =  
Round answer to 1 decimal place.

Explanation / Answer

1) for 70th percentile crtiical z =0.52

therefore corresponding value =mean+z*std deviaiton=1020+0.52*194=1120.88~ 1121

2)

ACT score =mean+z*std deviaiton=22.3+0.52*3.9=24.3

3)

ACT score =mean+z*std deviation=22.3+(1466-1020)*3.9/194=31.3

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