A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standar

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.

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Tài Đức 6 months 2021-07-17T03:57:36+00:00 1 Answers 5 views 0

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    2021-07-17T03:58:53+00:00

    Answer:

    The answer is “1110, 20.4, and 31.408

    Step-by-step 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 \times 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 \times 4.7 \\\\ =20.43585 \approx  20.4  

    For point c:

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

    Calculating equivalent ACT score:

    =19+2.64 \times 4.7 \\\\=31.408

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