High School

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The combined SAT scores for the students at a local high school are normally distributed with a mean of 1507 and a standard deviation of 301. The local college includes a minimum score of 1387 in its admission requirements.

What percentage of students from this school earn scores that satisfy the admission requirement?

\[ P(X > 1387) = \% \]

Answer :

Final answer:

Approximately 65.87% of the students from this school are likely to score above the college's minimum SAT score requirement of 1387, based on the normal distribution of scores at the school.

Explanation:

The subject of this question is Mathematics and it pertains to the concept of normal distribution. To answer the student's question, we need to first calculate the z-score of the SAT score using the formula Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

In this case, Z = (1387 - 1507) / 301 = -0.40. The z-score -0.40 corresponds to the 34.13 percentile on the standard normal distribution table. Because we are interested in the students scoring more than 1387, we subtract this value from 100, giving us 100 - 34.13 = 65.87%. Thus, approximate 65.87% of students from this school will earn a SAT score that satisfies the college's minimum requirement.

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