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 982 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5. 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 20-percentile, find the actual SAT score.SAT score =What would be the equivalent ACT score for this student?ACT score =If a student gets an SAT score of 1437, find the equivalent ACT score.ACT score =

Answer 1

Actual SAT Score = 815.284

Equivalent ACT Score = 15.811

The equivalent ACT Score = 29.95

Explanation:

From the given information:

Scores on the SAT test are normally distributed with :

Mean = 982

Standard deviation = 198

If a student gets an SAT score that is the 20-percentile

Then ;

P(Z ≤ z ) = 0.20

From the standard z-score for percentile distribution.

z = -0.842

Therefore, the actual SAT Score can be computed as follows:

Actual SAT score = Mean + (z score × Standard deviation)

Actual SAT score = 982 + (- 0.842 × 198)

Actual SAT score = 982 + ( - 166.716)

Actual SAT score = 982 - 166.716

Actual SAT Score = 815.284

Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5.

Mean = 19.6

Standard deviation = 4.5

Equivalent ACT Score = 19.6 + (- 0.842 × 4.5)

Equivalent ACT Score = 19.6 + ( - 3.789)

Equivalent ACT Score = 15.811

If a student gets an SAT score of 1437, find the equivalent ACT score.

So , if the SAT Score = 1437

Then , using the z formula , we can determine the equivalent ACT Score

`z = (X - \mu)/(\sigma)`

`z = (1437 - 982)/(198)`

`z = (455)/(198)`

z =2.30

The equivalent ACT Score = 19.6 + (2.30 × 4.5)

The equivalent ACT Score = 19.6 + 10.35

The equivalent ACT Score = 29.95