The combined SAT scores for the students at a local high school are normally distributed with a mean of 1519 and a standard deviation of 301. The local college includes a minimum score of 706 in its admission requirements.

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

\[ P(X > 706) = \, \_\_\_\_ \% \]

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 from this school who earn scores that satisfy the admission requirement, we need to convert the minimum score of 706 into a z-score using the given mean and standard deviation. Then, using a z-table or calculator, we can find the percentage of scores greater than that z-score.

Explanation:

To find the percentage of students from this school who earn scores that satisfy the admission requirement, we need to find the percentage of scores greater than 706, using the given mean and standard deviation.

First, we need to convert the score of 706 into a z-score using the formula:

z = (X - μ) / σ

Plugging in the values, we get:

z = (706 - 1519) / 301 = -2.44

Next, we can use a z-table or calculator to find the percentage of scores greater than -2.44. From the z-table, we find that the percentage is approximately 99.26%. Therefore, approximately 99.3% of students from this school earn scores that satisfy the admission requirement.

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