The combined SAT scores for the students at a local high school are normally distributed with a mean of 1480 and a standard deviation of 307. The local college includes a minimum score of 2278 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement?

P(X < 2278) = ____

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 find the percentage of students who earn scores that fail to satisfy the admission requirement, calculate the z-score and use a z-table or calculator.

Explanation:

To find the percentage of students who earn scores that fail to satisfy the admission requirement, we need to calculate the z-score corresponding to the minimum admission requirement. The z-score formula is (X - μ) / σ, where X is the minimum score requirement, μ is the mean, and σ is the standard deviation. Plugging in the values, we get the z-score as (2278 - 1480) / 307 = 2.587. Using a z-table or calculator, we can find the percentage associated with this z-score, which is approximately 99.6%. Therefore, about 99.6% of students from this school earn scores that fail to satisfy the admission requirement.

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