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 1051 and a standard deviation of 194. Scores on the ACT test are normally distributed with a mean of 19 and a standard deviation of 4.7. It is assumed that the two tests measure the same aptitude, but use different scales.

Required:
a. If a student gets an SAT score that is the 62-percentile, find the actual SAT score.
b. What would be the equivalent ACT score for this student?
c. If a student gets an SAT score of 1563, find the equivalent ACT score.

Answer 1

The answer is "1110, 20.4, and 31.408"

Explanation:

For point a:

Given:

`\to mean\ ( \bar{x})=1051\\\\\to standard \ deviation \ (\sigma)=194\\\\\to P(Z<=z)=0.62\\\\\to z=0.3055\\`

Calculating the SAT score:

`=1051+0.3055 * 194 \\\\ =1110.267 \approx 1110`

For point b:

Given:

`\to mean \ \bar{x}=19\\\\ \to standard \ deviation \ (\sigma) =4.7\\\\`

Calculating the equivalent ACT score:

`=19+0.3055 * 4.7 \\\\ =20.43585 \approx 20.4`

For point c:

`\to SAT \ Score =1563\\\\\to z=((1563-1051))/(194)= (512)/(194)=2.64\\\\`

Calculating equivalent ACT score:

`=19+2.64 * 4.7 \\\\=31.408`