Please help me on this question

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 1011 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 19.2 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 75-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 1407, find the equivalent ACT score.

ACT score =

Round answer to 1 decimal place.

Answer 1

To find the score that respresents the 75th percentile you need to refer to a normal table and find the z score that represents a probability of 0.7500. The appropriate z score is 0.675. To find the actual SAT score, use the following formula X = Zσ+μ, where σ is the standard deviation and μ is the mean for SAT scores

X = 0.675 * 198 + 1101 = 1235 rounded to the nearest whole number would be the 75th percentile.

To find the equivalent ACT score, use the ACT standard deviation and mean

X = 0.675 * 3.9 + 19.2 = 21.8

If a student scores 1407 on the SAT, we need to find the standardized score (z score) for 1407

z = (X-μ)/σ = (1407-1101)/198 = 1.545

The equivalent ACT score is found by using the formula from the first 2 parts of this question using 1.545 as the z score

X = 1.545 * 3.9 + 19.2 = 25.5

Please note, your answers may differ a bit based on how you are obtaining your z-scores from the normal table? Are you using the z-score whose probability is closest to .75 or are you interpolating? Instead of using a table, are you using a calculator or some statistical package and how many decimal places are you using?