The combined SAT scores for the students at a local high school are normally distributed with a mean of 1483 and a standard deviation of 294. The local college requires a minimum score of 1601 for admission.

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

Calculate $ P(X > 1601) $ and enter your answer as a percent accurate to 1 decimal place (do not include the "%" sign).

We calculate the z-score using the provided SAT score, mean and standard deviation. The z-score of 0.4 suggests that the score of 1601 is 0.4 standard deviations above the mean. Using a z-table, we find that approximately 34.5% of students from this school earn scores that satisfy the college's admission requirement.

Explanation:

To determine the percentage of students who earn scores that satisfy the admission requirement, we first need to calculate the z-score. The z-score is a statistical measure that tells us how many standard deviations an individual score is from the mean. It can be calculated using the following formula: z = (X - μ) / σ, where X is the score, μ is the mean and σ is the standard deviation.

Given in the question: X = 1601 (score requirement), μ = 1483 (mean score), and σ = 294 (standard deviation). Plugging these values into the formula, we get: z = (1601 - 1483) / 294 = 0.4.

This z-score tells us that the score of 1601 is 0.4 standard deviations above the mean. To determine the percentage of students who score at this level or higher, we need to look at tables or use software to find the probability associated with this z-score. The area to the right of z=0.4 in a standard normal distribution table is approximately 0.3446 or 34.46%.

Thus, approximately 34.5% of students from this school earn scores that satisfy the admission requirement.

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