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.

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codiepienagoya codiepienagoya · Answer 1 · 2021-02-22T08:01:29+01:00

Answer:

The answer is "1110, 20.4, and 31.408"

Step-by-step explanation:

For point a:

Given:

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

Calculating the SAT score:

[tex]=1051+0.3055 \times 194 \\\\ =1110.267 \approx 1110[/tex]

For point b:

Given:

[tex]\to mean \ \bar{x}=19\\\\ \to standard \ deviation \ (\sigma) =4.7\\\\[/tex]

Calculating the equivalent ACT score:

[tex]=19+0.3055 \times 4.7 \\\\ =20.43585 \approx 20.4[/tex]

For point c:

[tex]\to SAT \ Score =1563\\\\\to z=\frac{(1563-1051)}{194}= \frac{512}{194}=2.64\\\\[/tex]

Calculating equivalent ACT score:

[tex]=19+2.64 \times 4.7 \\\\=31.408[/tex]