Question

6)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 1047 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 21.4 and a standard deviation of 4.3. 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 55-percentile, find the actual SAT score.
SAT score =
(Round answer to a whole number.)

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

c)If a student gets an SAT score of 1251, find the equivalent ACT score.
ACT score =  
(Round answer to 1 decimal place.)

Answer 1

Answer:

To be in the 55-percentile need the z value that gives probability of 0.55

Going to the standard normal probabilities table 0.55 results in Z = 0.12566

z value is calculated by the sample score minus the mean divided by the standard deviation.

(a)

z = (x - µ)/sigma.

0.12566= (x - 1047)/204. Solving for  

x= 1072.635

Rounding to the nearest whole number gives the student's SAT score = 1073

(b)

The same process is

used for the ACT score. 0.12566 = (x - µ)/sigma. This time µ = 21.4 and sigma = 4.3

This gives the new equation 0.12566 = (x - 21.4)/4.3  Solving for x

x = 22

Rounding to the to 1 decimal place gives the student's ACT score = 22.0