High School

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 1019 and a standard deviation of 200. scores on the ACT test are normally distributed with a mean of 19.8 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 65-percentile, find the actual SAT score.
SAT score =
round answer to a whole number.

Answer :

A student's SAT score corresponding to the 65th percentile in a normally distributed set with a mean of 1019 and a standard deviation of 200 is 1097.

to find the SAT score corresponding to the 65th percentile in a normally distributed set with a mean of 1019 and a standard deviation of 200, you need to use the Z-score table.

The Z-score associated with the 65th percentile is approximately 0.39. Using the Z-score formula:

Z = (X - μ) / σ

We rearrange to solve for X (the SAT score):

X = Z * σ + μ

Plugging in the values:

X = 0.39 * 200 + 1019

X = 78 + 1019

X = 1097

Therefore, the SAT score at the 65th percentile is 1097.

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