The combined SAT scores for the students at a local high school are normally distributed with a mean of 1525 and a standard deviation of 290. The local college includes a minimum score of 1235 in its admission requirements.

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

[tex]P(X > 1235) = \, \%[/tex]

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

To determine the percentage of students that satisfy the SAT admission requirement, a z-score calculation is used. The result of this calculation shows that 84.1% of students from this school obtain SAT scores above the minimum score required by the local college.

Explanation:

The question is asking for the percentage of students who score above 1235 on the SAT - this translates to P(X > 1235). To solve this, we must calculate the z-score, which measures how many standard deviations an individual data point is from the mean.

The formula for calculating a z-score is Z = (X - μ) / σ, where X is your variable, μ is the mean, and σ is the standard deviation. For the given question, X = 1235, μ = 1525, and σ = 290. Using these values in the formula will give Z= (1235 - 1525) / 290, which is roughly -1.

Given that the Z table value for -1.0 is 0.1587, this tells us that 15.87% of students score below 1235. However, we're interested in the percentage of students who score above 1235, so we subtract 15.87% from 100%, giving us 84.1%. Therefore, 84.1% of students from this school earn scores that satisfy the admission requirement.

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